In this paper, a stochastic model for the turbulent fiber lay-down in the industrial production of nonwoven materials is extended by including a moving conveyor belt. In the hydrodynamic limit corresponding to large noise values, the transient and stationary joint probability distributions are determined using the method of multiple scales and the Chapman–Enskog method. Moreover, exponential convergence towards the stationary solution is proven for the reduced problem. For special choices of the industrial parameters, the stochastic limit process is an Ornstein–Uhlenbeck process. It is a good approximation of the fiber motion even for moderate noise values. Moreover, as shown by Monte-Carlo simulations, the limiting process can be used to assess the quality of nonwoven materials in the industrial application by determining distributions of functionals of the process.

}, author = {Bonilla, Luis L. and Götz, Thomas and Klar, Axel and Marheineke, Nicole and Wegener, Raimund}, doi = {10.1137/070692728}, faupublication = {no}, journal = {SIAM Journal on Applied Mathematics}, pages = {648-665}, peerreviewed = {Yes}, title = {{Hydrodynamic} limit for the {Fokker}-{Planck} equation describing fiber lay-down models}, volume = {68}, year = {2007} } @book{faucris.123797124, abstract = {Das Buch bietet detailliert und verständlich ausgearbeitete Lösungsvorschläge zu den 430 Aufgaben aus dem Buch "Mathematik für Ingenieure und Naturwissenschaftler, Lineare Algebra und Analysis in R". Zahlreiche dieser Lösungsvorschläge werden gesondert besprochen und analysiert, und bei einigen Aufgaben werden verschiedene Lösungswege vorgelegt.

Bedingt durch das breite Aufgabenspektrum, eignet sich dieses Lösungsbuch für eine Vielzahl von Studiengängen. Neben den Studierenden aus den Ingenieurstudiengängen, profitieren auch in besonderer Weise Mathematik- und Lehramtsstudierende von der Aufgabenvielfalt.}, address = {Berlin-Heidelberg}, author = {Merz, Wilhelm and Knabner, Peter}, doi = {10.1007/978-3-642-54529-0}, faupublication = {yes}, isbn = {978-3-642-54528-3}, peerreviewed = {unknown}, publisher = {Springer}, series = {Springer-Lehrbuch}, title = {{Endlich} gelöst! {Aufgaben} zur {Mathematik} für {Ingenieure} und {Naturwissenschaftler}}, url = {http://www.springer.com/us/book/9783642545283}, year = {2014} } @inproceedings{faucris.207760690, author = {Burger, Martin and et al.}, author_hint = {Burger M, Chu S, Markowich P, Schönlieb C}, booktitle = {PAMM Special Issue: ICIAM 07}, doi = {10.1002/pamm.200700802}, faupublication = {no}, note = {WWU::69510}, pages = {1011209-1011210}, peerreviewed = {No}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{Cahn}-{Hilliard} inpainting and the {Willmore} functional}, venue = {Zurich}, year = {2008} } @article{faucris.215930218, abstract = {In this paper, a model is developed for the evolution of plaques in arteries, which is one of the main causes for the blockage of blood flow. Plaque rupture and spread of torn-off material may cause closures in the down-stream vessel system and lead to ischemic brain or myocardial infarctions. The model covers the flow of blood and its interaction with the vessel wall. It is based on the assumption that the penetration of monocytes from the blood flow into the vessel wall, and the accumulation of foam cells increasing the volume, are main factors for the growth of plaques. The dynamics of the vessel wall is governed by a deformation gradient, which is given as composition of a purely elastic tensor, and a tensor modeling the biologically caused volume growth. An equation for the evolution of the metric is derived quantifying the changing geometry of the vessel wall. To calculate numerically the solutions of the arising free boundary problem, the model system of partial differential equations is transformed to an ALE (Arbitrary Lagrangian-Eulerian) formulation, where all equations are given in fixed domains. The numerical calculations are using newly developed algorithms for ALE systems. The results of the simulations, obtained for realistic system parameters, are in good qualitative agreement with observations. They demonstrate that the basic modeling assumption can be justified. The increase of stresses in the vessel wall can be computed. Medical treatment tries to prevent critical stress values, which may cause plaque rupture and its consequences.}, author = {Yang, Yifan and Jäger, Willi and Neuss-Radu, Maria and Richter, Thomas}, doi = {10.1007/s00285-015-0934-8}, faupublication = {yes}, journal = {Journal of Mathematical Biology}, keywords = {Atherosclerotic plaque formation;Fluid-structure interaction;Coupling biochemical reactions and biomechanics;Modeling tissue growth;Computing wall stresses}, pages = {973-996}, peerreviewed = {Yes}, title = {{Mathematical} modeling and simulation of the evolution of plaques in blood vessels}, volume = {72}, year = {2016} } @article{faucris.121985644, author = {Grün, Günther and Rauscher, Markus and Mecke, Klaus}, faupublication = {yes}, journal = {Journal of Statistical Physics}, pages = {1261-1291}, peerreviewed = {Yes}, title = {{Thin}-film flow influenced by thermal noise}, volume = {122}, year = {2006} } @article{faucris.116668684, author = {Grün, Günther and Becker, Jürgen}, faupublication = {no}, journal = {Proceedings in Applied Mathematics and Mechanics}, pages = {47-50}, peerreviewed = {Yes}, title = {{Some} remarks on modelling and simulation of thin-film flow}, volume = {4}, year = {2004} } @inproceedings{faucris.117790684, abstract = {We apply a novel upwind stabilization of a mixed hybrid finite element method of lowest order to advection–diffusion problemswith dominant advection and compare it with a finite element scheme stabilized by finite volume upwinding. Both schemes are locally mass conservative and employ an upwind-weighting formula in the discretization of the advective term. Numerical experiments indicate that the upwind-mixed method is competitive with the finite volume method. It prevents the appearance of spurious oscillations and produces nonnegative solutions for strongly advection-dominated problems, while the amount of artificial diffusion is lower than that of the finite volume method. This makes the method attractive for applications in which too much numerical diffusion is critical and may lead to false predictions; e.g., if highly nonlinear reactive processes take place only in thin interaction regions.}, author = {Brunner, Fabian and Frank, Florian and Knabner, Peter}, booktitle = {Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects}, date = {2014-06-15/2014-06-20}, doi = {10.1007/978-3-319-05684-5_16}, editor = {Fuhrmann Jürgen, Ohlberger Mario, Rohde Christian}, faupublication = {yes}, isbn = {9783319056838}, pages = {177-185}, peerreviewed = {unknown}, publisher = {Springer New York LLC}, title = {{FV} upwind stabilization of {FE} discretizations for advection-diffusion problems}, venue = {Berlin}, volume = {77}, year = {2014} } @book{faucris.121348524, abstract = {Ziel der Linearen Algebra ist die Einübung in die Theorie und Anwendung linearer Strukturen.

Der heutigen Bedeutung der Linearen Algebra als grundlegendes Werkzeug und Sprache für fast alle Teile der Mathematik entsprechend wurden die Inhalte bewußt breit gefasst und vernetzt:

Aspekte der affinen Geometrie (Lehramt), unendlich-dimensionale Vektorräume, Spektralanalyse und lineare Differentialgleichungen (Physik), allgemeine K-Vektorräume sowie algebraische Strukturen (Algebra), die Anfänge der linearen und quadratischen Optimierung (Wirtschaftsmathematik) und die LR-Zerlegung, Pseudoinverse und Singulärwertzerlegung (Numerische Mathematik und Optimierung).

Die erarbeitete Theorie und Algorithmik wird durchgängig mit innermathematischen Themen wie auch mit realen Anwendungen verbunden. Eine klare optische Struktur der Inhalte ermöglicht es dem Leser, den Kerntext von weiterführenden Bemerkungen leicht zu unterscheiden und somit das Buch als Lern- , Arbeits- wie auch als Nachschlagewerk zu benutzen.}, address = {Berlin-Heidelberg}, author = {Knabner, Peter and Barth, Wolf}, doi = {10.1007/978-3-642-32186-3}, edition = {1}, faupublication = {yes}, isbn = {978-3-642-32185-6}, peerreviewed = {unknown}, publisher = {Springer}, series = {Springer-Lehrbuch}, title = {{Lineare} {Algebra}: {Grundlagen} und {Anwendungen}}, url = {http://www.springer.com/de/book/9783642321856#aboutBook}, year = {2013} } @article{faucris.108972864, author = {Grün, Günther and Fischer, Julian}, faupublication = {yes}, journal = {SIAM Journal on Mathematical Analysis}, pages = {825-854}, peerreviewed = {Yes}, title = {{Finite} speed of propagation and waiting times for the stochastic porous medium equation -- a unifying approach}, volume = {47}, year = {2015} } @article{faucris.121946924, abstract = {The optimal design of rotational production processes for glass wool manufacturing poses severe computational challenges to mathematicians, natural scientists and engineers. In this paper we focus exclusively on the spinning regime where thousands of viscous thermal glass jets are formed by fast air streams. Homogeneity and slenderness of the spun fibers are the quality features of the final fabric. Their prediction requires the computation of the fluid-fiber-interactions which involves the solving of a complex three-dimensional multiphase problem with appropriate interface conditions. But this is practically impossible due to the needed high resolution and adaptive grid refinement. Therefore, we propose an asymptotic coupling concept. Treating the glass jets as viscous thermal Cosserat rods, we tackle the multiscale problem by help of momentum (drag) and heat exchange models that are derived on basis of slender-body theory and homogenization. A weak iterative coupling algorithm that is based on the combination of commercial software and self-implemented code for flow and rod solvers, respectively, makes then the simulation of the industrial process possible. For the boundary value problem of the rod we particularly suggest an adapted collocation-continuation method. Consequently, this work establishes a promising basis for future optimization strategies. © 2011 Springer-Verlag Berlin Heidelberg.}, author = {Arne, Walter and Marheineke, Nicole and Schnebele, Johannes and Wegener, Raimund}, doi = {10.1186/2190-5983-1-2}, faupublication = {yes}, journal = {Journal of Mathematics in Industry}, keywords = {boundary value problem; continuation method; Cosserat rods; drag models; fluid-fiber interactions; Rotational spinning process; slender-body theory; two-way coupling; viscous thermal jets}, pages = {1-26}, peerreviewed = {unknown}, title = {{Fluid}-fiber-interactions in rotational spinning process of glass wool production}, volume = {1}, year = {2011} } @article{faucris.113577244, author = {Grün, Günther and Bertsch, Michiel and Dal Passo, Roberta and Garcke, Harald}, faupublication = {no}, journal = {Advances in Differential Equations}, pages = {417-440}, peerreviewed = {unknown}, title = {{The} thin viscous flow equation in higher space dimensions}, volume = {3}, year = {1998} } @inproceedings{faucris.121307164, author = {Knabner, Peter and Schneid, Eckhard}, booktitle = {Numerical Modelling in Continuum Mechanics, Part II}, faupublication = {yes}, pages = {337–343}, title = {{Numerical} {Solution} of {Unsteady} {Saturated}/{Unsaturated} {Flow} {Through} {Porous} {Media}}, year = {1997} } @article{faucris.123748284, abstract = {Transport processes in groundwater systems with spatially heterogeneous properties often exhibit anomalous behavior. Using first-order approximations in velocity fluctuations we show that anomalous superdif-fusive behavior may result if velocity fields are modeled as superpositions of random space functions with correlation structures consisting of linear combinations of short-range correlations. In particular, this corresponds to the superposition of independent random velocity fields with increasing integral scales proposed as model for evolving scale heterogeneity of natural porous media [Gelhar, L. W. Water Resour. Res. 22 (1986), 135S-145S]. Monte Carlo simulations of transport in such multi-scale fields support the theoretical results and demonstrate the approach to superdiffusive behavior as the number of superposed scales increases.}, author = {Suciu, Nicolae and Attinger, Sabine and Radu, Adrian Florin and Vamo̧s, Cǎlin and Vanderborght, Jan and Vereecken, Harry and Knabner, Peter}, faupublication = {yes}, journal = {The Preprint-Series of the Institute of Applied Mathematics}, keywords = {Porous media; Random fields; Random walk; Transport}, pages = {1-18}, peerreviewed = {No}, title = {{Solute} transport in aquifers with evolving scale heterogeneity}, volume = {346}, year = {2011} } @article{faucris.205334628, abstract = {In dynamic imaging, a key challenge is to reconstruct image sequences with high temporal resolution from strong undersampling projections due to a relatively slow data acquisition speed. In this paper, we propose a variational model using the infimal convolution of Bregman distance with respect to total variation to model edge dependence of sequential frames. The proposed model is solved via an alternating iterative scheme, for which each subproblem is convex and can be solved by existing algorithms. The proposed model is formulated under both Gaussian and Poisson noise assumption and the simulation on two sets of dynamic images shows the advantage of the proposed method compared to previous methods.}, author = {Burger, Martin and et al.}, author_hint = {Ding QQ, Burger M, Zhang XQ}, doi = {10.1088/1361-6420/aa9a94}, faupublication = {no}, journal = {Inverse Problems}, keywords = {dynamic SPECT;sparsity;infimal convolution;Bregman distance;edge alignment;low rank representation}, month = {Jan}, peerreviewed = {Yes}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{Dynamic} {SPECT} reconstruction with temporal edge correlation}, url = {https://arxiv.org/pdf/1707.00158.pdf}, volume = {34}, year = {2018} } @unpublished{faucris.214979002, abstract = {

The aim of this paper is to establish a theory of nonlinear spectral decompositions in an infinite dimensional setting by considering the eigenvalue problem related to an absolutely one-homogeneous functional in a Hilbert space. This approach is motivated by works for the total variation and related functionals in , where some interesting results on the eigenvalue problem and the relation to the total variation flow have been proven previously, and by recent results on finite-dimensional polyhedral semi-norms, where gradient flows can yield exact decompositions into eigenvectors.

We provide a geometric characterization of eigenvectors via a dual unit ball, which applies to the infinite-dimensional setting and allows applications to several relevant examples. In particular our analysis highlights the role of subgradients of minimal norm and thus connects directly to gradient flows, whose time evolution can be interpreted as a decomposition of the initial condition into subgradients of minimal norm. We can show that if the gradient flow yields a spectral decomposition it is equivalent in an appropriate sense to other schemes such as variational methods with regularization parameter equal to time, and that the decomposition has an interesting orthogonality relation. Indeed we verify that all approaches where these equivalences were known before by other arguments--such as one-dimensional TV flow and multidimensional generalizations to vector fields or the gradient flow of certain polyhedral semi-norms--yield exact spectral decompositions, and we provide further examples. We also investigate extinction times and extinction profiles, which we characterize as eigenvectors in a very general setting, generalizing several results from literature.

},
author = {Bungert, Leon and Burger, Martin and Chambolle, Antonin and Novaga, Matteo},
faupublication = {yes},
note = {https://cris.fau.de/converis/publicweb/Publication/214979002},
peerreviewed = {automatic},
title = {{Nonlinear} {Spectral} {Decompositions} by {Gradient} {Flows} of {One}-{Homogeneous} {Functionals}},
url = {https://arxiv.org/abs/1901.06979},
year = {2019}
}
@inproceedings{faucris.111587784,
address = {Erlangen},
author = {Suciu, Nicolae and Vamos, Calin and Knabner, Peter and Rüde, Ulrich},
booktitle = {Simulationstechnique. 18th Symposium in Erlangen. September 2005},
faupublication = {yes},
isbn = {3-936150-41-9},
note = {UnivIS-Import:2015-04-16:Pub.2005.tech.IMMD.lsinfs.biased},
pages = {562-567},
publisher = {SCS Publishing House},
title = {{Biased} {Global} {Random} {Walk}, a {Cellular} {Automaton} for {Diffusion}},
venue = {Erlangen},
year = {2005}
}
@article{faucris.117799924,
abstract = {The objective of this research is to investigate the upscaling of flow and transport models including both an evolving solid-liquid interface and a quite general potentially even oscillating interaction potential. Starting from a comprehensive pore-scale model, formal, two-scale, asymptotic expansion in a level set framework is applied. In doing so, the interplay between flow, transport, interaction potential, and evolving geometry becomes evident. As a result of an averaging procedure, a fully coupled micro-macro model is established with new main variables. Moreover, time-and spacedependent coefficient functions are explicitly characterized by means of supplementary, fully coupled cell problems. The theoretical results obtained are complemented by the numerical computations of a heterogeneous multiscale scenario with a focus on the development of anisotropic transport. Because of the general framework considered in this research, numerous application are expected, such as in biology or colloidal dynamics.},
author = {Ray, Nadja and Elbinger, Tobias and Knabner, Peter},
doi = {10.1137/140990292},
faupublication = {yes},
journal = {SIAM Journal on Applied Mathematics},
keywords = {Evolving porous medium; Flow; Interaction potential; Level set; Transport; Two-scale asymptotic expansion; Upscaling},
pages = {2170-2192},
peerreviewed = {Yes},
title = {{Upscaling} the flow and transport in an evolving porous medium with general interaction potentials},
volume = {75},
year = {2015}
}
@inproceedings{faucris.123751584,
author = {Knabner, Peter and Summ, Gerhard},
booktitle = {Scientific Computing in Chemical Engineering II},
editor = {al. FK},
faupublication = {yes},
pages = {110-117},
peerreviewed = {unknown},
title = {{Hybrid} {Mixed} {Discretization} {Methods} for {Combustion} {Problems} in {Porous} {Media}},
url = {http://www.mso.math.fau.de/fileadmin/am1/users/knabner/publicationen/HybMixDiscCombPorMed_SCCE_99.pdf},
year = {1999}
}
@unpublished{faucris.214979280,
abstract = {In this work we investigate the computation of nonlinear eigenfunctions via the extinction profiles of gradient flows. We analyze a scheme that recursively subtracts such eigenfunctions from given data and show that this procedure yields a decomposition of the data into eigenfunctions in some cases as the 1-dimensional total variation, for instance. We discuss results of numerical experiments in which we use extinction profiles and the gradient flow for the task of spectral graph clustering as used, eg, in machine learning applications.We present convergence results for a fully discrete scheme based on the mixed finite element (MFE) method and an one-step Euler implicit (EI) method for simulating reactive solute transport in saturated/unsaturated soil. The results considered the low regularity of the solution of the degenerate parabolic equation describing the water flow in porous media.}, author = {Radu, Adrian Florin and Pop, Iuliu Sorin and Attinger, Sabine and Knabner, Peter}, faupublication = {yes}, journal = {Proceedings in Applied Mathematics and Mechanics}, pages = {1024705-1024706}, peerreviewed = {Yes}, title = {{Error} estimates for an {Euler} implicit-mixed finite element scheme for reactive transport in saturated/unsaturated soil}, volume = {7}, year = {2007} } @article{faucris.204148408, author = {Knodel, Markus and et al.}, author_hint = {Knodel M., Nägel A., Reiter S., Rupp M., Vogel A., Targett-Adams P., Herrmann E., Wittum G.}, doi = {10.1007/s00791-016-0261-7}, faupublication = {no}, journal = {Computing and Visualization in Science}, keywords = {Computational virology; Finite volumes; Multigrid}, pages = {235-253}, peerreviewed = {unknown}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{Multigrid} analysis of spatially resolved hepatitis {C} virus protein simulations}, volume = {17}, year = {2015} } @article{faucris.123784364, abstract = {Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.}, author = {Schüler, Lennart and Suciu, Nicolae and Knabner, Peter and Attinger, Sabine}, doi = {10.1016/j.advwatres.2016.06.012}, faupublication = {yes}, journal = {Advances in Water Resources}, keywords = {Global random walk; Heterogeneity; Mixing; PDF method; Solute transport; Variance}, pages = {55-67}, peerreviewed = {Yes}, title = {{A} time dependent mixing model to close {PDF} equations for transport in heterogeneous aquifers}, volume = {96}, year = {2016} } @incollection{faucris.117818184, abstract = {We consider a two-scale homogenized model for processes in living cells including reaction and diffusion inside and on the surface of organelles. The resulting equations are fully coupled and the number of biochemical species in applications is large. We developed numerical schemes in order to rcomputation time by means of better scaling on parallel machines and reduction of the problemsize. A combination of those schemes provides a suitable numerical framework for our problem.

phytoplankton, and zooplankton (NPZ) mode},
author = {Hajduk, Hennes and Hodges, Ben R and Aizinger, Vadym and Reuter, Balthasar},
doi = {10.1016/j.envsoft.2018.01.003},
faupublication = {yes},
journal = {ENVIRON MODELL SOFTW },
keywords = {Discontinuous Galerkin finite element method; Multi-component advection-reaction system; Transport scheme; NPZ model; Shallow water equations},
pages = {185-198},
peerreviewed = {Yes},
title = {{Locally} {Filtered} {Transport} for computational efficiency in multi-component advection-reaction models},
volume = {102},
year = {2018}
}
@book{faucris.206530978,
address = {Aachen},
author = {Prechtel, Alexander},
faupublication = {yes},
isbn = {3-8322-4295-3},
peerreviewed = {Yes},
publisher = {Shaker},
title = {{Modelling} and {Efficient} {Numerical} {Solution} of {Hydrogeochemical} {Multicomponent} {Transport} {Problems} by {Process}-{Preserving} {Decoupling} {Techniques}},
year = {2005}
}
@incollection{faucris.117979004,
abstract = {Mathematical models provide the starting point for the simulation of complex processes, which arise in the natural and engineering sciences. Characteristic properties of the considered systems are represented by model parameters or coefficients. These have to be determined by experiments. If the coefficients are not measured directly, as direct measurements are not possible or do not lead to satisfying results, numerical identification procedures have to be applied.},
address = {Berlin, Heidelberg},
author = {Knabner, Peter and Igler, B. A.},
booktitle = {Lectures on Applied Mathematics},
doi = {10.1007/978-3-642-59709-1_12},
editor = {Hans-Joachim Bungartz, Ronald H. W. Hoppe, Christoph Zenger},
faupublication = {yes},
isbn = {978-3-642-64094-0},
pages = {157-175},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Structural} {Identification} of {Nonlinear} {Coefficient} {Functions} in {Transport} {Processes} through {Porous} {Media}},
url = {http://link.springer.com/chapter/10.1007%2F978-3-642-59709-1_12},
year = {2000}
}
@article{faucris.117785624,
abstract = {In this paper we consider the Lagrange-Galerkin finite element approximation by continuous piecewise linears in space of the following problem: Given ω ⊂ R, 1 ≤ d ≤ 3, find u(x, t) and v(x, t) such that ∂u + ∂v - ∇.(D ∇u) + q.∇u = f in ω × (0, T], dv = k(φ(u) - v) in ω × (0, T], u(x, 0) = g(x), v(x, 0) = g(x) ∀ x ∈ ω, with periodic boundary conditions. Here k ∈ R and the spatial differential operator is uniformly elliptic, but φ ∈ C(R) ∩ C (-∞, 0] ∪ (0, ∞) is a monotonically increasing function satisfying φ(0) = 0, which is only locally Hölder continuous, with exponent p ∈ (0, 1) at the origin; e.g., ∈(s) := [s] . We obtain error bounds which improve on those in the literature.},
author = {Barrett, John W. and Knabner, Peter},
faupublication = {yes},
journal = {SIAM Journal on Numerical Analysis},
keywords = {Convection-dominated flow; Degenerate parabolic systems; Error analysis; Finite elements; Lagrange-galerkin; Modified method of characteristics; Porous medium},
pages = {1862-1882},
peerreviewed = {Yes},
title = {{An} improved error bound for a {Lagrange}-{Galerkin} method for contaminant transport with non-lipschitzian adsorption kinetics},
url = {http://epubs.siam.org/doi/pdf/10.1137/S0036142996301512},
volume = {35},
year = {1998}
}
@article{faucris.121944504,
abstract = {In this paper, we derive and investigate an asymptotic model for the dynamics of curved viscous inertial Newtonian fibres subjected to surface tension, as they occur in rotational spinning processes. Accordingly, we extend the slender body theory of Panda, Marheineke & Wegener (Math. Meth. Appl. Sci., vol. 31, 2008, p. 1153) by including surface tension and deducing boundary conditions for the free end of the fibre. The asymptotic model accounts for the inner viscous transport and places no restrictions on either the motion or the shape of the fibre centreline. Depending on the capillary number, the boundary conditions yield an explicit description for the temporal evolution of the fibre end. We study numerically the behaviour of the fibre as a function of the effects of viscosity, gravity, rotation and surface tension. © 2009 Cambridge University Press.},
author = {Marheineke, Nicole and Wegener, Raimund},
doi = {10.1017/S0022112008005259},
faupublication = {no},
journal = {Journal of Fluid Mechanics},
pages = {345-369},
peerreviewed = {Yes},
title = {{Asymptotic} model for the dynamics of curved viscous fibres with surface tension},
volume = {622},
year = {2009}
}
@article{faucris.123859824,
author = {Van Duijn, C. J. (Hans) and Knabner, Peter},
faupublication = {yes},
journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik},
pages = {329-332},
peerreviewed = {Yes},
title = {{Crystal} dissolution in porous media flow},
url = {https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=33749455829&origin=inward},
volume = {76},
year = {1996}
}
@article{faucris.117792664,
abstract = {We investigate the influence of aggregation and deposition on the colloidal dynamics in a saturated porous medium. On the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal mass splits into different size clusters and we treat clusters as different species involved in a diffusion-reaction mechanism. This modeling procedure allows for different material properties to be varied between the different species, specifically the diffusion rate, which changes due to size as described by the Stokes-Einstein relation, and the deposition rate. The periodic homogenization procedure is applied to obtain a macroscopic model. The resulting model is illustrated by numerical computations that capture the colloidal transport with and without aggregation.},
author = {Krehel, Oleh and Muntean, Adrian and Knabner, Peter},
doi = {10.1016/j.advwatres.2015.10.005},
faupublication = {yes},
journal = {Advances in Water Resources},
keywords = {Aggregation; Colloidal transport; Deposition; Multiscale coefficients; Periodic homogenization},
pages = {209-216},
peerreviewed = {Yes},
title = {{Multiscale} modeling of colloidal dynamics in porous media including aggregation and deposition},
volume = {86},
year = {2015}
}
@incollection{faucris.123320824,
abstract = {

}, author = {Liu, Chen and Frank, Florian and Rivière, Béatrice}, doi = {10.1002/num.22362}, faupublication = {yes}, journal = {Numerical Methods For Partial Differential Equations}, keywords = {Cahn–Hilliard equation; error analysis; interior penalty discontinuous Galerkin methods; stability analysis; unique solvability}, month = {Jan}, peerreviewed = {Yes}, title = {{Numerical} error analysis for nonsymmetric interior penalty discontinuous {Galerkin} method of {Cahn}–{Hilliard} equation}, year = {2019} } @article{faucris.201552267, abstract = {},
author = {Himmelsbach, Dominik and Neuss-Radu, Maria and Neuß, Nicolas},
doi = {10.1016/j.jmaa.2017.12.026},
faupublication = {yes},
journal = {Journal of Mathematical Analysis and Applications},
keywords = {Magnetic targeting; Magnetic field; Radially symmetrical solution; Quasilinear parabolic equations; Superparamagnetic nanoparticle},
pages = {1544-1560},
peerreviewed = {Yes},
title = {{Mathematical} modelling and analysis of nanoparticle gradients induced by magnetic fields},
volume = {461},
year = {2018}
}
@article{faucris.119195164,
author = {Igler, B. A. and Totsche, Kai Uwe and Knabner, Peter},
doi = {10.1016/S0079-1946(98)00016-0},
faupublication = {yes},
journal = {Physics and Chemistry of the Earth},
pages = {215-219},
peerreviewed = {unknown},
title = {{Identification} of {Nonlinear} {Sorption} {Isotherms} by {Soil} {Column} {Breakthrough} {Experiments}},
url = {http://www.sciencedirect.com/science/article/pii/S0079194698000160},
volume = {23},
year = {1998}
}
@incollection{faucris.123843324,
abstract = {In this paper we discuss some iterative approaches for solving the nonlinear algebraic systems encountered as fully discrete counterparts of some degenerate (fast diffusion) parabolic problems. After regularization, we combine a mixed finite element discretization with the Euler implicit scheme. For the resulting systems we discuss three iterative methods and give sufficient conditions for convergence.},
address = {Berlin, Heidelberg},
author = {Radu, Adrian Florin and Pop, Iuliu Sorin and Knabner, Peter},
booktitle = {Numerical Mathematics and Advanced Applications},
doi = {10.1007/978-3-540-34288-5_120},
editor = {Alfredo Bermúdez de Castro, Dolores Gómez, Peregrina Quintela, Pilar Salgado},
faupublication = {yes},
isbn = {978-3-540-34287-8},
pages = {1192-1200},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Newton} - {Type} {Methods} for the {Mixed} {Finite} {Element} {Discretization} of {Some} {Degenerate} {Parabolic} {Equations}},
year = {2006}
}
@incollection{faucris.118079764,
address = {Frankfurt a. M.},
author = {Knabner, Peter and Kräutle, Serge and Oßmann, Stephan and Prechtel, Alexander},
booktitle = {Statusseminar Forschungsverbund KORA - Kontrollierter natürlicher Rückhalt und Abbau von Schadstoffen bei der Sanierung kontaminierter Grundwässer und Böden},
editor = {Dechema},
faupublication = {yes},
isbn = {389746071X},
pages = {417-427},
peerreviewed = {unknown},
title = {{Modellierung} des reaktiven {Transports} von {Schadstoffen} in der (un-)gesättigten {Bodenzone} zur {Prognose} der natürlichen {Selbstreinigung} - {Komplexe} {Probleme} berechenbar machen},
year = {2005}
}
@incollection{faucris.123746744,
abstract = {We propose and study the numerical approximation of an advection-diffusion-reaction model equation by a modified Brezzi–Douglas–Marini mixed finite element method.Nonlinear advection is admitted, arising in complex and coupled flow and transport systems.In contrast to the classical variant of this approach, optimal second-order convergence of the scalar and the vector variable is ensured.No loss of rate of convergence due to the presence of the advection term is observed.},
address = {Berlin Heidelberg},
author = {Bause, Markus and Brunner, Fabian and Knabner, Peter and Radu, Adrian Florin},
booktitle = {Numerical Mathematics and Advanced Applications 2011},
doi = {10.1007/978-3-642-33134-3_27},
editor = {Andrea Cangiani, Ruslan L. Davidchack, Emmanuil Georgoulis, Alexander N. Gorban, Jeremy Levesley, Michael V. Tretyakov},
faupublication = {yes},
isbn = {978-3-642-33133-6},
pages = {247-255},
peerreviewed = {unknown},
publisher = {Springer},
title = {{An} {Improved} {Optimal} {Order} {Mixed} {Finite} {Element} {Method} for {Semilinear} {Transport} {Problems}},
url = {http://link.springer.com/chapter/10.1007%2F978-3-642-33134-3_27},
year = {2012}
}
@article{faucris.204143727,
author = {Aizinger, Vadym and Rupp, Andreas and Schütz, Jochen and Knabner, Peter},
doi = {10.1007/s10596-017-9682-8},
faupublication = {yes},
journal = {Computational Geosciences},
keywords = {Mixed discontinuous Galerkin method; Stability and error analysis; Local discontinuous Galerkin method; Instationary Darcy problem},
pages = {179-194},
peerreviewed = {Yes},
title = {{Analysis} of a mixed discontinuous {Galerkin} method for instationary {Darcy} flow},
volume = {22},
year = {2018}
}
@article{faucris.117788484,
abstract = {This paper deals with the analytical investigations of a nonstationary Darcy-Nernst-Planck-Poisson-type system which is a mathematical model describing electrolyte solutions. For this nonlinear fully coupled system of partial differential equations we proof existence and uniqueness of global weak solutions. Furthermore, we establish physical properties for the number densities such as nonnegativity and boundedness in L∞ ((0, T) × Ω). © 2012 WILEY-VCH Verlag GmbH & Co. KGaA.},
author = {Herz, Matthias and Ray, Nadja and Knabner, Peter},
doi = {10.1002/gamm.201210013},
faupublication = {yes},
journal = {GAMM Mitteilungen},
keywords = {Darcy-Nernst-Planck-Poisson system; Electro-hydrodynamics; Fixed point approach; Global existence; Moser iteration},
pages = {191-208},
peerreviewed = {unknown},
title = {{Existence} and uniqueness of a global weak solution of a {Darcy}-{Nernst}-{Planck}-{Poisson} system},
volume = {35},
year = {2012}
}
@article{faucris.204148791,
author = {Knodel, Markus and et al.},
author_hint = {Knodel M., Lemke B., Lampe M., Hoffer M., Gillmann C., Uder M., Hillengaß J., Bäuerle T., Wittum G.,},
doi = {10.1007/s00791-018-0292-3},
faupublication = {no},
journal = {Computing and Visualization in Science},
keywords = {Cave automatic virtual environment; Surface reconstruction; Surface rendering; Imaging; Postprocessing; Virtual reality; Volume rendering},
pages = {203-212},
peerreviewed = {unknown},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{Virtual} reality in advanced medical immersive imaging: a workflow for introducing virtual reality as a supporting tool in medical imaging},
volume = {18},
year = {2018}
}
@article{faucris.109001684,
author = {Grün, Günther and Fontelos, Marco Antonio and Jörres, Simon},
faupublication = {yes},
journal = {SIAM Journal on Mathematical Analysis},
pages = {527-563},
peerreviewed = {Yes},
title = {{On} a phase-field model for electrowetting and other electrokinetic phenomena},
volume = {43},
year = {2011}
}
@phdthesis{faucris.111348644,
author = {Kräutle, Serge},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{A} {Navier}-{Stokes} solver based on {CGBI} and the method of characteristics},
year = {2001}
}
@article{faucris.116433284,
author = {Grün, Günther and Eck, Christof and Fontelos, Marco Antonio and Klingbeil, Fabian and Vantzos, Orestis},
doi = {10.4171/IFB/211},
faupublication = {yes},
journal = {Interfaces and Free Boundaries},
pages = {259-290},
peerreviewed = {Yes},
title = {{A} phase-field model for electrowetting},
volume = {11},
year = {2009}
}
@incollection{faucris.123855424,
abstract = {In this paper we perform a numerical bifurcation analysis of a one-dimensional problem arising in premixed combustion in porous inert media. The analysis shows that multiple steady solutions may occur, that a minimal mass flow rate is required for steady combustion, and that solutions with complete combustion exist for a large range of mass flow rates. Moreover, we show that a jump discontinuity in porosity and cooling contributes to the stability of the combustion zone. The one-dimensional results are compared with computations for a corresponding two-dimensional problem. The qualitative agreement between the solutions is good along the cooling boundary, and satisfactory along the axis of symmetry. The one-dimensional problem can therefore be used as preparation for a more complex two-dimensional simulation.},
address = {Berlin, Heidelberg},
author = {De Neef, Michel J. and Knabner, Peter and Summ, Gerhard},
booktitle = {High Performance Scientific and Engineering Computing},
doi = {10.1007/978-3-642-60155-2_4},
editor = {Hans-Joachim Bungartz, Franz Durst, Christoph Zenger},
faupublication = {yes},
pages = {39-50},
peerreviewed = {unknown},
publisher = {Springer},
series = {Lecture Notes in Computational Science and Engineering},
title = {{Numerical} {Bifurcation} {Analysis} of {Premixed} {Combustion} in {Porous} {Inert} {Media}},
url = {http://link.springer.com/chapter/10.1007%2F978-3-642-60155-2_4},
volume = {8},
year = {1999}
}
@article{faucris.108992884,
author = {Grün, Günther and Campillo Funollet, Eduard and Klingbeil, Fabian},
faupublication = {yes},
journal = {SIAM Journal on Applied Mathematics},
pages = {1899-1925},
peerreviewed = {Yes},
title = {{On} modeling and simulation of electrokinetic phenomena in two-phase flow with general mass densities},
volume = {72},
year = {2012}
}
@article{faucris.117817084,
abstract = {Mathematical modeling of biochemical pathways is an important resource in Synthetic Biology, as the predictive power of simulating synthetic pathways represents an important step in the design of synthetic metabolons. In this paper, we are concerned with the mathematical modeling, simulation, and optimization of metabolic processes in biochemical microreactors able to carry out enzymatic reactions and to exchange metabolites with their surrounding medium. The results of the reported modeling approach are incorporated in the design of the first microreactor prototypes that are under construction. These microreactors consist of compartments separated by membranes carrying specific transporters for the input of substrates and export of products. Inside the compartments of the reactor multienzyme complexes assembled on nano-beads by peptide adapters are used to carry out metabolic reactions. The spatially resolved mathematical model describing the ongoing processes consists of a system of diffusion equations together with boundary and initial conditions. The boundary conditions model the exchange of metabolites with the neighboring compartments and the reactions at the surface of the nano-beads carrying the multienzyme complexes. Efficient and accurate approaches for numerical simulation of the mathematical model and for optimal design of the microreactor are developed. As a proof-of-concept scenario, a synthetic pathway for the conversion of sucrose to glucose-6-phosphate (G6P) was chosen. In this context, the mathematical model is employed to compute the spatio-temporal distributions of the metabolite concentrations, as well as application relevant quantities like the outflow rate of G6P. These computations are performed for different scenarios, where the number of beads as well as their loading capacity are varied. The computed metabolite distributions show spatial patterns, which differ for different experimental arrangements. Furthermore, the total output of G6P increases for scenarios where microcompartimentation of enzymes occurs. These results show that spatially resolved models are needed in the description of the conversion processes. Finally, the enzyme stoichiometry on the nano-beads is determined, which maximizes the production of glucose-6-phosphat},
author = {Elbinger, Tobias and Gahn, Markus and Hante, Falk and Voll, Lars and Leugering, Günter and Knabner, Peter and Neuss-Radu, Maria},
doi = {10.3389/fbioe.2016.00013},
faupublication = {yes},
journal = {Frontiers in Bioengineering and Biotechnology},
peerreviewed = {Yes},
title = {{Model}-{Based} {Design} of {Biochemical} {Microreactors}},
year = {2016}
}
@article{faucris.108977484,
abstract = {By methods from nonequilibrium thermodynamics, we derive a diffuse interface

model for two-phase flow of incompressible fluids with dissolved noninteracting

polymers. The polymers are modeled by dumbbells subjected to general elastic springforce

potentials including in particular Hookean and finitely extensible, nonlinear elastic

(FENE) potentials. Their density and orientation are described by a Fokker-Planck-type

equation which is coupled to a Cahn-Hilliard and a momentum equation for phase-field

and gross velocity/pressure. Henry-type energy functionals are used to describe different

solubility properties of the polymers in the different phases or at the liquid-liquid interface.

Taking advantage of the underlying energetic/entropic structure of the system, we

prove existence of a weak solution globally in time for the case of FENE-potentials. As

a by-product in the case of Hookean spring potentials, we derive a macroscopic diffuse interface

model for two-phase flow of Oldroyd-B-type liquids.}, author = {Grün, Günther and Metzger, Stefan}, doi = {10.1142/S0218202516500196}, faupublication = {yes}, journal = {Mathematical Models & Methods in Applied Sciences}, pages = {823-866}, peerreviewed = {Yes}, title = {{On} micro-macro-models for two-phase flow with dilute polymeric solutions -- modeling and analysis}, volume = {26}, year = {2016} } @incollection{faucris.116676164, author = {Rivero-Rodriguez, Javier and Arne, Walter and Marheineke, Nicole and Wegener, Raimund and Pérez-Saborid, Miguel}, booktitle = {Progress in Industrial Mathematics at ECMI 2014}, faupublication = {yes}, peerreviewed = {unknown}, publisher = {Springer}, title = {{Setup} of viscous {Cosserat} rod model desribing electrospinning}, year = {2016} } @incollection{faucris.122038884, author = {Marheineke, Nicole and Wegener, Raimund}, booktitle = {Progress in Industrial Mathematics at ECMI 2010}, editor = {M. Günther, A. Bartel, M. Brunk, S. Schöps, M. Striebel}, faupublication = {yes}, pages = {239-246}, peerreviewed = {unknown}, publisher = {Springer}, title = {{Stochastic} {PDAE}-models and associated {Monte}-{Carlo} simulations for elastic threads in turbulent flows}, year = {2012} } @article{faucris.117796404, abstract = {We analyze a discretization method for a class of degenerate parabolic problems that includes the Richards' equation. This analysis applies to the pressure-based formulation and considers both variably and fully saturated regimes. To overcome the difficulties posed by the lack in regularity, we first apply the Kirchhoff transformation and then integrate the resulting equation in time. We state a conformal and a mixed variational formulation and prove their equivalence. This will be the underlying idea of our technique to get error estimates. A regularization approach is combined with the Euler implicit scheme to achieve the time discretization. Again, equivalence between the two formulations is demonstrated for the semidiscrete case. The lowest order Raviart-Thomas mixed finite elements are employed for the discretization in space. Error estimates are obtained, showing that the scheme is convergent. © 2004 Society for Industrial and Applied Mathematics.}, author = {Radu, Adrian Florin and Pop, Iuliu Sorin and Knabner, Peter}, doi = {10.1137/S0036142902405229}, faupublication = {yes}, journal = {SIAM Journal on Numerical Analysis}, keywords = {De-generate parabolic problems; Error estimates; Euler implicit scheme; Mixed finite elements; Porous media; Regularization; Richards' equation}, pages = {1452-1478}, peerreviewed = {Yes}, title = {{Order} of convergence estimates for an {Euler} implicit, mixed finite element discretization of {Richards}' equation}, volume = {42}, year = {2004} } @article{faucris.113569984, author = {Grün, Günther and Abels, Helmut and Garcke, Harald}, faupublication = {yes}, journal = {Mathematical Models & Methods in Applied Sciences}, pages = {1150013-1150052}, peerreviewed = {Yes}, title = {{Thermodynamically} consistent diffuse interface models for incompressible two-phase flows with different densities}, volume = {22}, year = {2012} } @article{faucris.116639644, abstract = {We present and investigate techniques for optimizing particle dispersions in all kinds of Reynolds number flows. In particular, we show the range of application, power and efficiency of space mapping approaches that are based on a hierarchy of models ranging from a complex (fine, accurate, costly) to simple (coarse, rough, cheap) model. Space mapping turns out to be a reasonable approximation to optimal control and a competitive alternative to instantaneous control regarding speed and memory demands when dealing with complex, non-stationary problems. Moreover it allows the easy and efficient treatment of stochastic design problems. To control random particle dynamics in a turbulent flow, we suggest a Monte-Carlo aggressive space mapping algorithm which yields very convincing numerical results. © 2011 Springer Science+Business Media, LLC.}, author = {Marheineke, Nicole and Pinnau, René and Reséndiz, Edgar}, doi = {10.1007/s11081-011-9150-6}, faupublication = {yes}, journal = {Optimization and Engineering}, keywords = {Instantaneous control; k-ε{lunate} turbulence model; Navier-Stokes equations; Optimal control; Particle dynamics; Space mapping technique; Stochastic control; Tracking problem}, pages = {101-120}, peerreviewed = {Yes}, title = {{Space} mapping-focused control techniques for particle dispersions in fluids}, volume = {13}, year = {2012} } @article{faucris.119186584, abstract = {A multi-level method for the determination of nonlinear coefficient functions of parabolic partial differential equations is presented as an example of the reconstruction of the hydraulic properties of porous media from soil column outflow experiments. A linear stability and error analysis is used to characterize the ill-posedness of the inverse problem. Founded on this analysis, optimal experimental design problems can be formulated. Numerical examples are presented which show that the method described leads to a stable solution of the inverse problem.}, author = {Bitterlich, Sandro and Knabner, Peter}, doi = {10.1088/0266-5611/19/5/302}, faupublication = {yes}, journal = {Inverse Problems}, pages = {1011-1030}, peerreviewed = {Yes}, title = {{Experimental} design for outflow experiments based on a multi-level identification method for material laws}, volume = {19}, year = {2003} } @article{faucris.216729740, author = {Grün, Günther and Grillmeier, Hubertus}, doi = {10.1090/mcom/3372}, faupublication = {yes}, journal = {Mathematics of Computation}, pages = {1021-1059}, peerreviewed = {Yes}, title = {{Nonnegativity} preserving convergent schemes for the stochastic porous-medium equation}, year = {2018} } @inproceedings{faucris.208634631, abstract = {The accurate simulation of realistic flow scenarios is still a challenging problem, and a final answer has not yet been found. Nevertheless, flow simulations are nowadays ubiquitous during the design process of vehicles like aircrafts or cars, as well as in many other fields of science and engineering. Ideally such simulations should run in real-time and should be easily available to everyone. We have started to work in that direction last year when setting up an interactive web application for calculating the flow around a two-dimensional user-drawn airfoil using the finite element library Femlisp (http://www.femlisp.org).

The

pCO2, dissolved inorganic carbon (DIC), and*δ*13CDIC data were used to determine CO2 outgassing from an acidic headwater stream in the Uhlířská catchment (Czech Republic). This stream drains a catchment with silicate bedrock. The applied stable isotope model is based on the principle that the 13C ∕ 12C ratio of its sources and the intensity of CO2 outgassing control the isotope ratio of DIC in stream water. It avoids the use of the gas transfer velocity parameter (*k*), which is highly variable and mostly difficult to constrain. Model results indicate that CO2 outgassing contributed more than 80 % to the annual stream inorganic carbon loss in the Uhlířská catchment. This translated to a CO2 outgassing rate from the stream of 34.9 kg C m−2 yr−1 when normalised to the stream surface area. Large temporal variations with maximum values shortly before spring snowmelt and in summer emphasise the need for investigations at higher temporal resolution. We improved the model uncertainty by incorporating groundwater data to better constrain the isotope compositions of initial DIC. Due to the large global abundance of acidic, humic-rich headwaters, we underline the importance of this integral approach for global applications.

and dissolution and precipitation of immobile species present inside a porous medium. The

transport of mobile species in the pores is modeled by a system of semilinear parabolic

partial differential equations. The reactions amongst the mobile species are assumed to

be reversible, i.e. both forward and backward reactions are considered. These reversible

reactions lead to highly nonlinear reaction rate terms on the right-hand side of the partial

differential equations. This system of equations for the mobile species is complemented

by flux boundary conditions at the outer boundary. Furthermore, the dissolution and

precipitation of immobile species on the surface of the solid parts are modeled by mass

action kinetics which lead to a nonlinear precipitation term and a multivalued dissolution

term. The model is posed at the pore (micro) scale. The contribution of this paper is two-

fold: first we show the existence of a unique positive global weak solution for the coupled

systems and then we upscale (homogenize) the model from the micro scale to the macro

scale. For the existence of solution, some regularization techniques, Schaefer’s fixed point

theorem and Lyapunov type arguments have been used whereas the concepts of two-scale

convergence and periodic unfolding are used for the homogenization.

p) the travelling wave may exist. For*p* ≤ 1, the travelling wave always exists, whereas for 1 < *p* ≤ 2 it depends on the values of the other adsorption parameters and whether a lower bound of the upstream concentration (at *x* = −∞) is exceeded. For *p* ≥ 2, the existence of the travelling wave requires that the upstream concentration does not exceed an (specified) upper bound. Besides illustrating some waves we show that two different rate functions that have the Freundlich isotherm as their limit for an infinite rate parameter result in qualitatively different travelling waves.},
author = {Van Duijn, C. J. (Hans) and Knabner, Peter and van der Zee, Sjoerd E. A. T. M.},
doi = {10.1016/0309-1708(93)90001-V},
faupublication = {no},
journal = {Advances in Water Resources},
keywords = {Transport; travelling wave; porous media; Langmuir isotherm; Freundlich isotherm; non-linear adsorption},
pages = {97-105},
peerreviewed = {Yes},
title = {{Travelling} waves during the transport of reactive solute in porous media: {Combination} of {Langmuir} and {Freundlich} isotherms},
url = {http://www.sciencedirect.com/science/article/pii/030917089390001V},
volume = {16},
year = {1993}
}
@article{faucris.117790464,
abstract = {The authors study concentration profiles of solutes undergoing equilibrium absorption in the vicinity of a water well. For the case of a contamination event, the limit problem of vanishing well radius, which is of self-similar nature, is analysed in detail. Existence, uniqueness, and qualitative properties of solutions of the corresponding ordinary differential equations are shown. Some numerical examples are also presented. © 1994 Oxford University Press.},
author = {Van Duijn, C. J. (Hans) and Knabner, Peter},
doi = {10.1093/imamat/52.2.177},
faupublication = {yes},
journal = {IMA Journal of Applied Mathematics},
pages = {177-200},
peerreviewed = {Yes},
title = {{Flow} and reactive transport in porous media induced by well injection: {Similarity} solution},
volume = {52},
year = {1994}
}
@incollection{faucris.116687164,
author = {Arne, Walter and Marheineke, Nicole and Wegener, Raimund},
booktitle = {Progress in Industrial Mathematics at ECMI 2010},
editor = {M. Günther A. Bartel, M. Brunk, S. Schöps, M. Striebel},
faupublication = {yes},
pages = {349-356},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Asymptotic} models of different complexity for viscous jets and their applicability regimes},
year = {2012}
}
@article{faucris.204146716,
abstract = {Investigation of cellular and network dynamics in the brain by means of modeling and simulation has evolved into a highly interdisciplinary field, that uses sophisticated modeling and simulation approaches to understand distinct areas of brain function. Depending on the underlying complexity, these models vary in their level of detail, in order to cope with the attached computational cost. Hence for large network simulations, single neurons are typically reduced to time-dependent signal processors, dismissing the spatial aspect of each cell. For single cell or networks with relatively small numbers of neurons, general purpose simulators allow for space and time-dependent simulations of electrical signal processing, based on the cable equation theory. An emerging field in Computational Neuroscience encompasses a new level of detail by incorporating the full three-dimensional morphology of cells and organelles into three-dimensional, space and time-dependent, simulations. While every approach has its advantages and limitations, such as computational cost, integrated and methods-spanning simulation approaches, depending on the network size could establish new ways to investigate the brain. In this paper we present a hybrid simulation approach, that makes use of reduced 1D-models using e.g., the NEURON simulatorwhich couples to fully resolved models for simulating cellular and sub-cellular dynamics, including the detailed three-dimensional morphology of neurons and organelles. In order to couple 1D- and 3D-simulations, we present a geometry-, membrane potential- and intracellular concentration mapping framework, with which graph- based morphologies, e.g., in the swc- or hoc-format, are mapped to full surface and volume representations of the neuron and computational data from 1D-simulations can be used as boundary conditions for full 3D simulations and vice versa. Thus, established models and data, based on general purpose 1D-simulators, can be directly coupled to the emerging field of fully resolved, highly detailed 3D-modeling approaches. We present the developed general framework for 1D/3D hybrid modeling and apply it to investigate electrically active neurons and their intracellular spatio-temporal calcium dynamics.},
author = {Knodel, Markus and et al.},
author_hint = {Grein S, Stepniewski M, Reiter S, Knodel MM, Queisser G},
doi = {10.3389/fninf.2014.00068},
faupublication = {no},
journal = {Frontiers in Neuroinformatics},
keywords = {calcium dynamics;electrical stimulation;hybrid;parallel;detailed modeling;intracellular signaling;neuron;PDEs},
peerreviewed = {unknown},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{1D}-{3D} hybrid modelingfrom multi-compartment models to full resolution models in space and time},
volume = {8},
year = {2014}
}
@article{faucris.117784304,
abstract = {[1] A new systematic approach for the efficient computation of the transport and reaction of a multispecies multireaction system is developed. The objective of this approach is to reduce the number of coupled nonlinear differential equations drastically, while splitting errors are avoided. The reduction mechanism is able to handle both kinetic reactions and heterogeneous equilibrium reactions and mobile and immobile species. It leads to a formulation of the nonlinear system with a Jacobian that has very few nonzero entries. Applications of the reduction mechanism to reaction networks, including a biodegradation problem which is modeled by the Monod approach, are given. Two numerical examples demonstrate the speed up of the presented reduction mechanism. Copyright 2005 by the American Geophysical Union.},
author = {Kräutle, Serge and Knabner, Peter},
doi = {10.1029/2004WR003624},
faupublication = {yes},
journal = {Water Resources Research},
pages = {1-17},
peerreviewed = {Yes},
title = {{A} new numerical reduction scheme for fully coupled multicomponent transport-reaction problems in porous media},
volume = {41},
year = {2005}
}
@article{faucris.116618524,
abstract = {The paper at hand presents a combination of optimal control approaches for PDEs with meshless discretizations. Applying a classical Lagrangian type particle method to optimization problems with hyperbolic constraints, several adjoint-based strategies differing in the sequential order of optimization and discretization of the Lagrangian or Eulerian problem formulation are proposed and compared. The numerical results confirm the theoretically predicted independence principle of the optimization approaches and show the expected convergence behavior. Moreover, they exemplify the superiority of meshless methods over the conventional mesh-based approaches for the numerical handling and optimization of problems with time-dependent geometries and freely moving boundaries. © 2011 Elsevier B.V. All rights reserved.},
author = {Marburger, Jan and Marheineke, Nicole and Pinnau, René},
doi = {10.1016/j.cam.2010.12.018},
faupublication = {yes},
journal = {Journal of Computational and Applied Mathematics},
keywords = {Adjoint method; EulerianLagrangian formulation; Hyperbolic equations; Meshless methods; Optimization strategies; Particle methods},
pages = {3138-3150},
peerreviewed = {Yes},
title = {{Adjoint}-based optimal control using meshfree discretizations},
volume = {235},
year = {2011}
}
@article{faucris.121947584,
abstract = {Considering the dynamics of long slender elastic fibers in turbulent flows, there exists a stochastic aerodynamic force concept for a general drag model based on a k- ε{lunate} turbulence description in literature. In this paper we generalize the concept and formulate an air drag model that is universally valid for all Reynolds number regimes and incident flow directions. The associated turbulent force overcomes the hitherto existing limitations and allows the simulation of all kind of fibers (flexible, stiff, light, heavy) immersed in turbulent flows. Moreover, the comparison of the numerical results with PIV-measurements shows very convincing agreements in the industrial application of technical textile manufacturing. © 2010 Elsevier Ltd.},
author = {Marheineke, Nicole and Wegener, Raimund},
doi = {10.1016/j.ijmultiphaseflow.2010.10.001},
faupublication = {yes},
journal = {International Journal of Multiphase Flow},
keywords = {Aerodynamic drag; Data interpolation; Dimensional analysis; Fiber-fluid interactions; Long slender fibers; Numerical simulations; Stochastic partial differential algebraic equation; Turbulence modeling},
pages = {136-148},
peerreviewed = {Yes},
title = {{Modeling} and application of a stochastic drag for fibers in turbulent flows},
volume = {37},
year = {2011}
}
@article{faucris.217583073,
abstract = {The article concerns the growth of biofilms made by chemotactical bacteria within a saturated porous media. The increase of a biomass on the surface of the solid matrix changes the porosity and impedes the flow through the pores. By formal periodic homogenization we derive an averaged model describing the process via Darcy's law and upscaled transport equations with effective coefficients given by the evolving microstructure at the pore-scale. Based on the assumption of uniform evolve of the underlying pore geometry and slight self-diffusivity of the bacteria, solvability in a weak sense global in time or at least up to a possible clogging phenomenon is shown in the two-dimensional case. Furthermore,},
author = {Schulz, Raphael and Knabner, Peter},
doi = {10.1137/16M108817X},
faupublication = {yes},
journal = {SIAM Journal on Applied Mathematics},
keywords = {biofilm growth;chemotaxis;porous media;fluid-solid interactions;evolving microstructure;parabolic PDE},
month = {Jan},
pages = {1653-1677},
peerreviewed = {Yes},
title = {{AN} {EFFECTIVE} {MODEL} {FOR} {BIOFILM} {GROWTH} {MADE} {BY} {CHEMOTACTICAL} {BACTERIA} {IN} {EVOLVING} {POROUS} {MEDIA}},
volume = {77},
year = {2017}
}
@incollection{faucris.208631534,
author = {Neuß, Nicolas},
booktitle = {Abschlussbericht SFB 359},
doi = {10.1007/978-3-540-28396-6_21},
editor = {Universität Heidelberg},
faupublication = {no},
isbn = {9783540283799},
pages = {567-577},
peerreviewed = {unknown},
publisher = {Springer Berlin Heidelberg},
title = {{High}-accuracy approximation of effective coefficients},
year = {2007}
}
@book{faucris.204149148,
author = {Knodel, Markus and et al.},
author_hint = {Knodel M., Nägel A., Reiter S., Rupp M., Vogel A., Lampe M., Targett-Adams P., Herrmann E., Wittum G.},
doi = {10.1007/978-3-319-24633-8_41},
faupublication = {no},
isbn = {9783319246338},
pages = {641-657},
peerreviewed = {Yes},
publisher = {Springer International Publishing},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{On} estimation of a viral protein diffusion constant on the curved intracellular {ER} surface},
year = {2016}
}
@article{faucris.208169582,
abstract = {A numerical method is formulated for the solution of the advective Cahn–Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on the exterior boundary. The CH equation describes phase separation of an immiscible binary mixture at constant temperature in the presence of a mass constraint and dissipation of free energy. Porous media/pore-scale problems specifically entail images of rocks in which the solid matrix and pore spaces are fully resolved. The interior penalty discontinuous Galerkin method is used for the spatial discretization of the CH equation in mixed form, while a semi-implicit convex–concave splitting is utilized for temporal discretization. The spatial approximation order is arbitrary, while it reduces to a finite volume scheme for the choice of elementwise constants. The resulting nonlinear systems of equations are reduced using the Schur complement and solved via inexact Newton's method. The numerical scheme is first validated using numerical convergence tests and then applied to a number of fundamental problems for validation and numerical experimentation purposes including the case of degenerate mobility. First-order physical applicability and robustness of the numerical method are shown in a breakthrough scenario on a voxel set obtained from a micro-CT scan of a real sandstone rock sample.

R4 on top of a k-*ε* turbulence description and describe the interactions in the context of slender-body theory as one-way-coupling with a corresponding stochastic aerodynamic drag force on the fibers. Hereby we exploit the special covariance structure of the random field, namely isotropy, homogeneity and decoupling of space and time. In this work we will focus on the construction and efficient simulation of the turbulent fluctuations assuming constant flow parameters and give an outlook on applications.},
author = {Hübsch, Florian and Marheineke, Nicole and Wegener, Raimund},
booktitle = {Progress in Industrial Mathematics at ECMI 2012},
doi = {10.1007/978-3-319-05365-3_16},
editor = {Magnus Fontes, Michael Günther, Nicole Marheineke},
faupublication = {yes},
isbn = {978-3-319-05364-6},
pages = {119-126},
peerreviewed = {unknown},
publisher = {Springer},
series = {Mathematics in Industry},
title = {{Efficient} simultaion of random fields for fiber-fluid interactions in isotropic turbulence},
volume = {19},
year = {2014}
}
@article{faucris.124247464,
abstract = {In this article, an approach for the efficient numerical solution of multi-species reactive transport problems in porous media is described. The objective of this approach is to reformulate the given system of partial and ordinary differential equations (PDEs, ODEs) and algebraic equations (AEs), describing local equilibrium, in such a way that the couplings and nonlinearities are concentrated in a rather small number of equations, leading to the decoupling of some linear partial differential equations from the nonlinear system. Thus, the system is handled in the spirit of a global implicit approach (one step method) avoiding operator splitting techniques, solved by Newton's method as the basic algorithmic ingredient. The reduction of the problem size helps to limit the large computational costs of numerical simulations of such problems. If the model contains equilibrium precipitation-dissolution reactions of minerals, then these are considered as complementarity conditions and rewritten as semismooth equations, and the whole nonlinear system is solved by the semismooth Newton method. © Springer Science + Business Media B.V. 2009.},
author = {Hoffmann, Joachim and Kräutle, Serge and Knabner, Peter},
doi = {10.1007/s10596-009-9173-7},
faupublication = {yes},
journal = {Computational Geosciences},
keywords = {Complementarity problems; Numerical simulation; Porous media; Reactive transport; Size reduction},
pages = {421-433},
peerreviewed = {Yes},
title = {{A} parallel global-implicit 2-{D} solver for reactive transport problems in porous media based on a reduction scheme and its application to the {MoMaS} benchmark problem},
volume = {14},
year = {2010}
}
@masterthesis{faucris.122809764,
author = {Kräutle, Serge},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Approximationen} der {Navier}-{Stokes}-{Gleichungen} mit {Finiten} {Differenzen}},
year = {1996}
}
@article{faucris.205335427,
abstract = {We consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. An example of this class of models is the so-called Kucken-Champod model describing the formation of fingerprint patterns. This class of models can be regarded as a generalization of a gradient flow of a nonlocal interaction potential which has a local repulsion and a long-range attraction structure. In contrast to isotropic interaction models the anisotropic forces in our class of models cannot be derived from a potential. The underlying tensor field introduces an anisotropy leading to complex patterns which do not occur in isotropic models. This anisotropy is characterized by one parameter in the model. We study the variation of this parameter, describing the transition between the isotropic and the anisotropic model, analytically and numerically. We analyze the equilibria of the corresponding mean-field partial differential equation and investigate pattern formation numerically in two dimensions by studying the dependence of the parameters in the model on the resulting patterns.},
author = {Burger, Martin and et al.},
author_hint = {Burger M, During B, Kreusser LM, Markowich PA, Schonlieb CB},
doi = {10.1142/S0218202518500112},
faupublication = {no},
journal = {Mathematical Models & Methods in Applied Sciences},
keywords = {Nonlocal interactions;pattern formation;dynamical systems},
pages = {409-451},
peerreviewed = {Yes},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{Pattern} formation of a nonlocal, anisotropic interaction model},
url = {https://arxiv.org/pdf/1610.08108.pdf},
volume = {28},
year = {2018}
}
@article{faucris.216552999,
abstract = {The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation result, dynamical properties of the SDE can be rigorously pulled back via the discrete scheme to the original Ensemble Kalman inversion. The results of this paper make a step towards closing the gap of the missing approximation result by proving a strong convergence result in a simplified model of a scalar SDE. We focus here on a toy model with similar properties to the one arising in the context of an Ensemble Kalman filter. The proposed model can be interpreted as a single particle filter for a linear map and thus forms the basis for further analysis. The difficulty in the analysis arises from the formally derived limiting SDE with nonglobally Lipschitz continuous nonlinearities both in the drift and in the diffusion. Here the standard Euler-Maruyama scheme might fail to provide a strongly convergent numerical scheme and taming is necessary. In contrast to the strong taming usually used, the method presented here provides a weaker form of taming. We present a strong convergence analysis by first proving convergence on a domain of high probability by using a cutoff or localization, which then leads, combined with bounds on moments for both the SDE and the numerical scheme, by a bootstrapping argument to strong convergence.},
author = {Wacker, Philipp Konstantin and Blömker, Dirk and Schillings, Claudia},
doi = {10.1137/17M1132367},
faupublication = {yes},
journal = {SIAM Journal on Numerical Analysis},
keywords = {Ensemble Kalman filter;stochastic differential equations;Bayesian inverse problems},
month = {Jan},
pages = {2537-2562},
peerreviewed = {Yes},
title = {{A} {STRONGLY} {CONVERGENT} {NUMERICAL} {SCHEME} {FROM} {ENSEMBLE} {KALMAN} {INVERSION}},
volume = {56},
year = {2018}
}
@article{faucris.215929141,
abstract = {In this paper, we consider a system of reaction-diffusion equations in a domain consisting of two bulk regions separated by a thin layer with thickness of order epsilon and a periodic heterogeneous structure. The equations inside the layer depend on epsilon and the diffusivity inside the layer on an additional parameter gamma is an element of [-1, 1]. On the bulk-layer interface, we assume a nonlinear Neumann-transmission condition depending on the solutions on both sides of the interface. For epsilon -> 0, when the thin layer reduces to an interface Sigma between two bulk domains, we rigorously derive macroscopic models with effective conditions across the interface Sigma. The crucial part is to pass to the limit in the nonlinear terms, especially for the traces on the interface between the different compartments. For this purpose, we use the method of two-scale convergence for thin heterogeneous layers, and a Kolmogorov-type compactness result for Banach valued functions, applied to the unfolded sequence in the thin layer.},
author = {Gahn, Markus and Neuss-Radu, Maria and Knabner, Peter},
doi = {10.3934/nhm.2018028},
faupublication = {yes},
journal = {Networks and Heterogeneous Media},
keywords = {Homogenization;nonlinear transmission conditions;reaction-diffusion systems;effective interface conditions;unfolding and averaging operator for thin heterogeneous layer;weak and strong two-scale convergence},
pages = {609-640},
peerreviewed = {Yes},
title = {{EFFECTIVE} {INTERFACE} {CONDITIONS} {FOR} {PROCESSES} {THROUGH} {THIN} {HETEROGENEOUS} {LAYERS} {WITH} {NONLINEAR} {TRANSMISSION} {AT} {THE} {MICROSCOPIC} {BULK}-{LAYER} {INTERFACE}},
volume = {13},
year = {2018}
}
@article{faucris.204938769,
abstract = {This is the first in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source MATLAB/GNU Octave toolbox. The intention of this ongoing project is to provide a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix/vector operations and is carefully documented; in addition, a direct mapping between discretization terms and code routines is maintained throughout. The present work focuses on a two-dimensional time-dependent diffusion equation with space/time-varying coefficients. The spatial discretization is based on the local discontinuous Galerkin formulation. Approximations of orders zero through four based on orthogonal polynomials have been implemented; more spaces of arbitrary type and order can be easily accommodated by the code structure. (C) 2015 Elsevier Ltd. All rights reserved.},
author = {Frank, Florian and Reuter, Balthasar and Aizinger, Vadym and Knabner, Peter},
doi = {10.1016/j.camwa.2015.04.013},
faupublication = {yes},
journal = {Computers & Mathematics With Applications},
keywords = {MATLAB; GNU Octave; local discontinuous Galerkin method; vectorization; open source},
pages = {11–46},
peerreviewed = {Yes},
title = {{FESTUNG}: {A} {MATLAB}/{GNU} {Octave} toolbox for the discontinuous {Galerkin} method, {Part} {I}: {Diffusion} operator},
volume = {70},
year = {2015}
}
@incollection{faucris.119675644,
author = {Marheineke, Nicole},
booktitle = {Progress in Industrial Mathematics at ECMI 2008},
editor = {A. Fitt, J. Norbury, H. Ockendon, E. Wilson},
faupublication = {yes},
pages = {589-590},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Models} and methods for viscous jets, break-up and drop forming},
year = {2010}
}
@article{faucris.117797284,
abstract = {The appropriate prediction of the fate of the contaminant is an essential step when evaluating the risk of severe groundwater pollutions - in particular in the context of natural attenuation. We numerically study the reactive transport of phenanthrene at the field scale in a multilayer soil profile based on experimental data. The effect of carrier facilitation by dissolved organic carbon is emphasized and incorporated in the model. Previously published simulations are restricted to the saturated zone and/or to homogeneous soil columns at the laboratory scale. A numerical flow and transport model is extended and applied to understand and quantify the relevant processes in the case of a strongly sorbing hydrophobic organic compound that is subject to carrier facilitation in the unsaturated zone. The contaminant migration is investigated on long- and short-term time scales and compared to predictions without carrier facilitation. The simulations demonstrate the importance of carrier facilitation and suggest strongly to take this aspect into account. By carrier facilitation breakthrough times at the groundwater level decreased from 500 to approximately 8 years and concentration peaks increased by two orders of magnitude in the long-term simulation assuming a temporary spill in an initially unpolluted soil with a non-sorbing carrier. © 2002 Elsevier Science B.V. All rights reserved.},
author = {Prechtel, Alexander and Knabner, Peter and Schneid, Eckhard and Totsche, Kai Uwe},
doi = {10.1016/S0169-7722(01)00211-X},
faupublication = {yes},
journal = {Journal of Contaminant Hydrology},
keywords = {Carrier facilitation; Dissolved organic matter; Hydrophobic organic compounds; Numerical transport model; Unsaturated flow},
pages = {209-225},
peerreviewed = {Yes},
title = {{Simulation} of carrier-facilitated transport of phenanthrene in a layered soil profile},
volume = {56},
year = {2002}
}
@article{faucris.211506717,
abstract = {The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the regularised solutions and allow us to obtain convergence rates in terms of Bregman distances-as usual in inverse problems, under an additional assumption on the exact solution called the source condition. These results are obtained for general absolutely one-homogeneous functionals. In the special case of TV-based regularisation we also study the structure of regularised solutions and prove convergence of their level sets to those of an exact solution. Finally, using the developed theory, we adapt the concept of debiasing to inverse problems with imperfect operators and propose an approach to pointwise error estimation in TV-based regularisation.},
author = {Burger, Martin and Korolev, Yury and Rasch, Julian},
doi = {10.1088/1361-6420/aaf6f5},
faupublication = {yes},
journal = {Inverse Problems},
note = {CRIS-Team WoS Importer:2019-02-21},
peerreviewed = {Yes},
title = {{Convergence} rates and structure of solutions of inverse problems with imperfect forward models},
volume = {35},
year = {2019}
}
@article{faucris.122013804,
author = {Grün, Günther},
faupublication = {no},
journal = {Interfaces and Free Boundaries},
pages = {309-323},
peerreviewed = {Yes},
title = {{Droplet} spreading under weak slippage: the optimal asymptotic propagation rate in the multi-dimensional case},
volume = {4},
year = {2002}
}
@article{faucris.119486444,
abstract = {Upscaling transport in porous media including both biomass development and simultaneous structural changes in the solid matrix is extremely challenging. This is because both affect the medium's porosity as well as mass transport parameters and flow paths. We address this challenge by means of a multiscale model. At the pore scale, the local discontinuous Galerkin (LDG) method is used to solve differential equations describing particularly the bacteria's and the nutrient's development. Likewise, a sticky agent tightening together solid or bio cells is considered. This is combined with a cellular automaton method (CAM) capturing structural changes of the underlying computational domain stemming from biomass development and solid restructuring. Findings from standard homogenization theory are applied to determine the medium's characteristic time- and space-dependent properties. Investigating these results enhances our understanding of the strong interplay between a medium's functional properties and its geometric structure. Finally, integrating such properties as model parameters into models defined on a larger scale enables reflecting the impact of pore scale processes on the larger scale. (C) 2017 Elsevier Ltd. All rights reserved.},
author = {Ray, Nadja and Rupp, Andreas and Prechtel, Alexander},
doi = {10.1016/j.advwatres.2017.04.001},
faupublication = {yes},
journal = {Advances in Water Resources},
keywords = {Soil structure;Biomass development;Transport properties;Mathematical modeling;Cellular automaton;Multiscale methods},
pages = {393-404},
peerreviewed = {Yes},
title = {{Discrete}-continuum multiscale model for transport, biomass development and solid restructuring in porous media},
volume = {107},
year = {2017}
}
@article{faucris.207688144,
abstract = {The phase-field method is a versatile and robust technique for modeling interfacial motion in multiphase flows in pore-scale media. The method provides an effective way to account for surface effects by use of diffuse interfaces. The resulting model significantly simplifies the numerical implementation of mass transport and momentum balance solvers for simulating two-phase flow with a large number of moving interfaces. The interfaces can be generated, transported or destroyed based on a thermodynamic Helmholtz free-energy minimization framework underpinning the governing equations. The phase-field method accurately conserves mass and is relatively straightforward to implement in conjunction with contact angle models that account for wettability on rock surfaces. The underlying free-energy minimization framework leads to the advective Cahn-Hilliard equation and modified Navier-Stokes equations that describe the phase-field model.

We have implemented a particular variant of the phase-field method (PFM) into the computational core of a pore-scale multiphase flow simulator, namely PMFS-PFM, for the numerical simulations of incompressible flows of two immiscible fluid phases. The implementation was discussed in a previous paper for rectangular prism-shaped fully-connected domains, e.g., for simulating two-phase flow in a 2D slit or a 3D duct (Alpak et al., 2016). In this paper, we discuss the recent developments on PMFS-PFM. The main components of the new work are (I) implementation of support for inactive cells in PMFS-PFM by extending the original finite-volume method-based discretizations of the underlying partial differential equations (PDEs) in order to solve realistic 3D pore-scale flow problems on rock volumes stemming from imaging, and (II) enhancing the performance of the simulator through implementation of modern sparse linear solvers and distributed parallel computing. It has been shown that the simulations performed on complex pore-scale domains are consistent with the physics of the immiscible two-phase displacement. The parallel scalability of the code is reasonably well varying between 50% and 86% on the investigated test cases of varying complexity. Results indicate that the more disconnected the pore-scale domains, the lower the parallel efficiency. It has been noted that there is a possibility of improving the parallel efficiency by exploring various grid subdivisions.

An extension of the Lagrange-Galerkin approach is developed for advection-dominated problems with nonlinear adsorption, either being in equilibrium or in non-equilibrium, possibly with isotherms of the Freundlich type. The scheme should be feasable also for the hyperbolic limit case. The basic problems to deal with are the possibility of non-unique characteristics due to the nonlinear isotherms and the incorporation of the time-dependent non-equilibrium adsorption kinetics, avoiding a strong restriction on the CFL-number.

The one-dimensional scheme derived is able to handle shock solutions. In the non-equilibrium case a more severe restriction on the timestep has to be regarded.

}, address = {Braunschweig, Wiesbaden}, author = {Barrett, John W. and Kappmeier, H. and Knabner, Peter}, booktitle = {Modeling and Computation in Environmental Sciences}, doi = {10.1007/978-3-322-89565-3_4}, editor = {Rainer Helmig, Willi Jäger, Wolfgang Kinzelbach, Peter Knabner, Gabriel Wittum}, faupublication = {yes}, pages = {36-48}, peerreviewed = {unknown}, publisher = {Vieweg+Teubner}, series = {Notes on Numerical Fluid Mechanics}, title = {{Lagrange}-{Galerkin} {Approximation} {For} {Advection}-{Dominated} {Contaminant} {Transport} {With} {Nonlinear} {Equilibrium} {Or} {Non}-equilibrium {Adsorption}}, url = {http://link.springer.com/chapter/10.1007%2F978-3-322-89565-3_4}, volume = {59}, year = {1997} } @inproceedings{faucris.215928880, abstract = {We consider a system of non-linear reaction diffusion equations in a domain consisting of two bulk regions separated by a thin layer with periodic structure. The thickness of the layer is of order is an element of, and the equations inside the layer depend on the parameter is an element of and an additional parameter gamma is an element of[-1, 1), which describes the size of the diffusion in the layer. We derive effective models for the limit is an element of -> 0, when the layer reduces to an interface Sigma between the two bulk domains. The effective solution is continuous across Sigma for all gamma is an element of [-1, 1). For gamma is an element of(-1, 1), the jump in the normal flux is given by a non-linear ordinary differential equation on Sigma. In the critical case gamma = -1, a dynamic transmission condition of Wentzell-type arises at the interface Sigma.}, author = {Gahn, Markus and Neuss-Radu, Maria and Knabner, Peter}, doi = {10.3934/dcdss.2017039}, faupublication = {yes}, keywords = {Thin heterogeneous layer;homogenization;weak and strong two-scale convergence;non-linear reaction-diffusion systems;effective transmission conditions}, pages = {773-797}, peerreviewed = {Yes}, publisher = {AMER INST MATHEMATICAL SCIENCES-AIMS}, title = {{DERIVATION} {OF} {EFFECTIVE} {TRANSMISSION} {CONDITIONS} {FOR} {DOMAINS} {SEPARATED} {BY} {A} {MEMBRANE} {FOR} {DIFFERENT} {SCALING} {OF} {MEMBRANE} {DIFFUSIVITY}}, volume = {10}, year = {2017} } @article{faucris.108689504, abstract = {This paper presents methods for the time-dependent numerical solution of a two-dimensional model governing combustion an inert porous media. The spatial discretization is based on a mixed finite element method for the flow problem and a cell-centered finite volume scheme for the transport equations. Some results of numerical simulations show the influence of a jump in the porosity of the solid matrix on the localization of the combustion zone.}, author = {Knabner, Peter and De Neef, Michel J. and Summ, Gerhard}, doi = {10.1002/zamm.19990791312}, faupublication = {yes}, journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik}, pages = {45-48}, peerreviewed = {Yes}, title = {{Transient} {Numerical} {Simulation} of {Combustion} in {Inert} {Porous} {Media}}, volume = {79}, year = {1999} } @article{faucris.210415617, abstract = {Hyperspectral imaging is a cutting-edge type of remote sensing used for mapping vegetation properties, rock minerals and other materials. A major drawback of hyperspectral imaging devices is their intrinsic low spatial resolution. In this paper, we propose a method for increasing the spatial resolution of a hyperspectral image by fusing it with an image of higher spatial resolution that was obtained with a different imaging modality. This is accomplished by solving a variational problem in which the regularization functional is the directional total variation. To accommodate for possible mis-registrations between the two images, we consider a non-convex blind super-resolution problem where both a fused image and the corresponding convolution kernel are estimated. Using this approach, our model can realign the given images if needed. Our experimental results indicate that the non-convexity is negligible in practice and that reliable solutions can be computed using a variety of different optimization algorithms. Numerical results on real remote sensing data from plant sciences and urban monitoring show the potential of the proposed method and suggests that it is robust with respect to the regularization parameters, mis-registration and the shape of the kernel.}, author = {Bungert, Leon and Ehrhardt, Matthias Joachim and Coomes, David and Rasch, Jennifer and Reisenhofer, Rafael and Schönlieb, Carola-Bibiane}, doi = {10.1088/1361-6420/aaaf63}, faupublication = {yes}, journal = {Inverse Problems}, keywords = {remote sensing;super-resolution;pansharpening;blind deconvolution;hyperspectral imaging}, peerreviewed = {Yes}, title = {{Blind} image fusion for hyperspectral imaging with the directional total variation}, volume = {34}, year = {2018} } @article{faucris.123853224, abstract = {We prove optimal order convergence of an upwind-mixed hybrid finite element scheme for linear parabolic advection-diffusion-reaction problems. It was introduced in [Radu et al., Adv. Water Resources, 34(2011), pp. 47-61] and is based on an Euler-implicit mixed hybrid finite element discretization of the problem in fully mass conservative form using the Raviart-Thomas mixed finite element of lowest order on triangular meshes. Optimal order convergence in time and space is obtained for the fully discrete formulation. The scheme provides the same order of convergence as the standard upwind-mixed method, while it is more efficient since a local elimination of variables is possible with our choice of the upwind weights. The theoretical findings are sustained by a numerical experiment. © 2014 Society for Industrial and Applied Mathematics.}, author = {Brunner, Fabian and Radu, Adrian Florin and Knabner, Peter}, doi = {10.1137/130908191}, faupublication = {yes}, journal = {SIAM Journal on Numerical Analysis}, keywords = {A priori error estimates; Advection-diffusion problem; Advection-dominance; Mixed finite element method; Upwind weighting}, pages = {83-102}, peerreviewed = {Yes}, title = {{Analysis} of an upwind-mixed hybrid finite element method for transport problems}, volume = {52}, year = {2014} } @article{faucris.117793764, abstract = {The evaluation of contaminated sites with respect to their potential for natural attenuation to relevant orders of magnitude in concentration and reasonable time scales requires estimating future plume behaviour. In this regard, model simulations are a valuable tool, e.g. through studies of predictive scenarios, but they have to fulfil demanding criteria that common software codes often cannot meet. We first present an overview of work completed within the framework of the joint research project BayFoNA in the domain of modelling. The herein described universal software tool is capable of reflecting the relevant processes of contaminant propagation and transformation, including, for example carrier facilitation or general temperature dependent decay reactions. Due to site heterogeneity, highly localized reactions, as well as aspects including nonlinearity or varying time scales, the quality of the numerical methods can have a decisive influence on the assessment of the natural attenuation potential. Therefore non standard locally mass conservative finite element discretizations were applied, employing functions of higher order to reduce numerical dispersion (which, in some cases, may lead to an overestimation of microbial degradation), or a globally implicit solution algorithm to avoid splitting errors and convergence problems. The simulation tool also allows the identification of unknown parameters by well defined experiments. Applications in the joint research project demonstrate the implementation of the techniques in the case of BTEX contamination, and helped clarify issues related to the migration of arsenic.}, author = {Prechtel, Alexander and Bitterlich, Sandro and Radu, Adrian Florin and Knabner, Peter}, doi = {10.1007/s00767-006-0147-6}, faupublication = {yes}, journal = {Grundwasser}, pages = {217-225}, peerreviewed = {Yes}, title = {{Natural} {Attenuation}: hohe {Anforderungen} an die {Modellsimulation} {Teilprojekt} 6 des {BayFoNA}: {Modellierung}}, volume = {11}, year = {2006} } @article{faucris.106667044, author = {Grün, Günther and Fontelos, Marco Antonio}, faupublication = {yes}, journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik}, pages = {777-788}, peerreviewed = {Yes}, title = {{On} uniqueness results for an elliptic-parabolic system of pde arising in dynamic electrowetting}, volume = {93}, year = {2013} } @phdthesis{faucris.123816484, author = {Marheineke, Nicole}, faupublication = {no}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Turbulent} {Fibers} - {On} the {Motion} of {Long} {Flexible} {Fibers} in {Turbulent} {Flows}}, year = {2005} } @incollection{faucris.117962724, abstract = {Numerical simulations have become an important tool to predict the evolution of groundwater and subsurface contamination by organic compounds. Due to the observation of sharp interfaces on which biochemical degradation of the contaminants takes place, a reliable and accurate prognosis requires high spatial resolution of the considered subsurface domain and/or the application of higher order discretization methods. A successfull realization of these simulations can only be provided by parallel computer systems with high computing power and memory availability. In this article, our concepts and simulation results of “real world” scenarios of organic contamination are presented.}, address = {Berlin, Heidelberg}, author = {Kräutle, Serge and Bause, Markus and Prechtel, Alexander and Radu, Adrian Florin and Knabner, Peter}, booktitle = {High Performance Computing in Science and Engineering, Garching 2004}, doi = {10.1007/3-540-28555-5_16}, editor = {Arndt Bode, Franz Durst}, faupublication = {yes}, isbn = {978-3-540-26145-2}, pages = {181-192}, peerreviewed = {unknown}, publisher = {Springer}, title = {{ParRichy}: {Parallel} {Simulation} of {Bioreactive} {Multicomponent} {Transport} {Processes} in {Porous} {Media}}, year = {2005} } @incollection{faucris.106884184, abstract = {The reliable prediction of the fate of contaminants in the subsurface is a demanding task for modelers in the environmental sciences. We present a simulation tool that is capable of handling a variety of complex scenarios that are of interest for site remediation or natural attenuation. The modular model components include the Richards equation for (un-) saturated fluid flow which is discretized by locally mass conserving hybrid mixed finite elements. The transport equations contain (nonlinear) terms for equilibrium or kinetic sorption processes and biodegradation reactions. Microbial processes may be described by first order reactions leading to linear reaction networks or a multiplicative dual Monod model including electron donator, electron acceptor and biomass. Simulation of carrier facilitation or surfactant transport (including associated permeability changes and effects on surface tension of the fluid) are feasible as well. The systems of equations are treated with Newton's method and adaptive techniques are applied to improve the efficiency of the implementation. We present an example of coupled surfactant migration and fluid flow. Current and future work includes the application to column experiments to investigate the potential of contaminated sites for natural attenuation and the extension of the model to geochemical multicomponent transport. © 2002 Elsevier B.V. All rights reserved.}, author = {Prechtel, Alexander and Knabner, Peter}, booktitle = {Computational Methods in Water Resources}, doi = {10.1016/S0167-5648(02)80125-3}, editor = {S. Majid Hassanizadeh, Ruud J. Schotting, William G. Gray and George F. Pinder}, faupublication = {yes}, isbn = {978-0-444-50975-8}, pages = {687-694}, peerreviewed = {unknown}, series = {Computational Methods in Water Resources, Proceedings of the XIV International Conference on Computational Methods in Water Resources (CMWR XIV)}, title = {{Accurate} and efficient simulation of coupled water flow and nonlinear reactive transport in the saturated and vadose zone-application to surfactant enhanced and intrinsic bioremediation}, volume = {47}, year = {2002} } @article{faucris.215225684, abstract = {Segmentation is one of the fundamental tasks in computer vision applications. For natural images there exist a vast amount of sophisticated segmentation methods in the literature. However, these standard methods tend to fail in the presence of non-Gaussian image noise, e.g., in biomedical imaging or astronomy. In this paper we propose an adequate variational segmentation model for segmentation of images perturbed by arbitrary noise models without adding a-priori assumptions about the unknown physical noise model. For this, we discuss the prominent minimal surface problem and two different numerical minimization schemes to solve it. The first approach efficiently computes the set of all possible minimal surface solutions for the given data via convex optimization and reduces the segmentation problem to the estimation of a proper threshold. The second approach is based on level set methods and is especially suitable for the separation of inhomogeneous image regions. The advantage of this approach is both its simpleness and robustness: the noise in the data does not have to be modeled explicitly since the image intensities are separated using histogram-based thresholding techniques. The proposed model can be interpreted as a generalization of many traditional segmentation methods which implicitly assume a perturbation by additive Gaussian noise. The superiority of this approach over standard methods such as the popular Chan–Vese formulation is demonstrated on synthetic images as well as real application data from biomedical imaging.
We investigate a spatially discrete surrogate model for the dynamics of a slender, elastic, inextensible fiber in turbulent flows. Deduced from a continuous space-time beam model for which no solution theory is available, it consists of a high-dimensional second order stochastic differential equation in time with a nonlinear algebraic constraint and an associated Lagrange multiplier term. We establish a suitable framework for the rigorous formulation and analysis of the semi-discrete model and prove existence and uniqueness of a global strong solution. The proof is based on an explicit representation of the Lagrange multiplier and on the observation that the obtained explicit drift term in the equation satisfies a one-sided linear growth condition on the constraint manifold. The theoretical analysis is complemented by numerical studies concerning the time discretization of our model. The performance of implicit Euler-type methods can be improved when using the explicit representation of the Lagrange multiplier to compute refined initial estimates for the Newton method applied in each time step.

}, author = {Lindner, Felix and Marheineke, Nicole and Stroot, Holger and Vibe, Alexander and Wegener, Raimund}, doi = {10.1142/S0219493717500162}, faupublication = {yes}, journal = {Stochastics and Dynamics}, keywords = {Stochastic elastic beam dynamics; stochastic differential algebraic equation; manifold-valued stochastic differential equation; nonlinear constraint; global solution theory}, peerreviewed = {Yes}, title = {{Stochastic} dynamics for inextensible fibers in a spatially semi-discrete setting}, year = {2016} } @article{faucris.117795524, abstract = {In this work we present and analyze a reliable and robust approximation scheme for biochemically reacting transport in the subsurface following Monod type kinetics. Water flow is modeled by the Richards equation. The proposed scheme is based on higher order finite element methods for the spatial discretization and the two step backward differentiation formula for the temporal one. The resulting nonlinear algebraic systems of equations are solved by a damped version of Newton's method. For the linear problems of the Newton iteration Krylov space methods are used. In computational experiments conducted for realistic subsurface (groundwater) contamination scenarios we show that the higher order approximation scheme significantly reduces the amount of inherent numerical diffusion compared to lower order ones. Thereby an artificial transverse mixing of the species leading to a strong overestimation of the biodegradation process is avoided. Finally, we present a robust adaptive time stepping technique for the coupled flow and transport problem which allows efficient long-term predictions of biodegradation processes. © Springer-Verlag 2004.}, author = {Bause, Markus and Knabner, Peter}, doi = {10.1007/s00791-004-0139-y}, faupublication = {yes}, journal = {Computing and Visualization in Science}, pages = {61-78}, peerreviewed = {unknown}, title = {{Numerical} simulation of contaminant biodegradation by higher order methods and adaptive time stepping}, volume = {7}, year = {2004} } @article{faucris.119221344, abstract = {In this paper we present a rigorous error analysis for the Lagrange-Galerkin method applied to convection-dominated diffusion problems. We prove new error estimates in which the constants depend on norms of the data and not of the solution and do not tend to infinity in the hyperbolic limit. This is in contrast to other results in this field. For the time discretization, uniform convergence with respect to the diffusion parameter of order O(k/t) is shown for initial values in L and O(k) for initial values in H. For the spatial discretization with linear finite elements, we verify uniform convergence of order O(h + min{h, h/k}) for data in H. By interpolation of Banach spaces, suboptimal convergence rates are derived under less restrictive assumptions. The analysis is heavily based on a priori estimates, uniform in the diffusion parameter, for the solution of the continuous and the semidiscrete problem. They are derived in a Lagrangian framework by transforming the Eulerian coordinates completely into subcharacteristic coordinates. Finally, we illustrate the error estimates by some numerical results.}, author = {Bause, Markus and Knabner, Peter}, doi = {10.1137/S0036142900367478}, faupublication = {yes}, journal = {SIAM Journal on Numerical Analysis}, keywords = {ε-uniform convergence; Characteristics; Convection-diffusion equation; Finite element method; Lagrange-Galerkin scheme}, pages = {1954-1984}, peerreviewed = {Yes}, title = {{Uniform} error analysis for {Lagrange}-{Galerkin} approximations of convection-dominated problems}, volume = {39}, year = {2002} } @article{faucris.116621164, abstract = {This work deals with the modeling and simulation of non-Newtonian jet dynamics as it occurs in fiber spinning processes. Proceeding from a three-dimensional instationary boundary value problem of upper-convected Maxwell equations, we present a strict systematic derivation of a one-dimensional viscoelastic string model by using asymptotic analysis in the slenderness ratio of the jet. The model allows for the unrestricted motion and shape of the jet's curve, and its deduction extends the hitherto existing uniaxial asymptotic approaches. However, the system of partial differential equations with algebraic constraint has a varying character (hyperbolic, hyperbolic-elliptic, parabolic deficiency). Its applicability range turns out to be limited depending on the physical parameters and the boundary conditions (i.e. singular perturbation). Numerical results are discussed for the hyperbolic regime of gravitational inflow-outflow set-ups which become relevant in drawing and extrusion processes. The simulations are performed with a normal form total upwind scheme in space and an implicit time-integration ensuring convergence of first order.}, author = {Marheineke, Nicole and Liljegren-Sailer, Björn and Lorenz, Maike and Wegener, Raimund}, doi = {10.1142/S021820251650010X}, faupublication = {yes}, journal = {Mathematical Models & Methods in Applied Sciences}, keywords = {asymptotic expansions; Curved viscoelastic jets; normal form total upwind scheme; slender body theory; upper-convected Maxwell model}, pages = {569-600}, peerreviewed = {Yes}, title = {{Asymptotics} and numerics for the upper-convected {Maxwell} model describing transient curved viscoelastic jets}, volume = {26}, year = {2016} } @article{faucris.123853664, abstract = {A drug delivery system, named minirod, containing insoluble non-cross-linked collagen was prepared to investigate the release of model drug compounds. To characterise the complete drug release process properly, a mathematical model was developed. Previously, a mathematical model describing water penetration, matrix swelling and drug release by diffusion from dense collagen matrices has been introduced and tested. However, enzymatic matrix degradation influences the drug release as well. Based on experimental data, a model was developed which describes drug release by collagenolytic matrix degradation based on enzyme diffusion, adsorption and cleavage. Data for swelling, collagen degradation and FITC dextran release from insoluble equine collagen type I minirods were collected. Sorption studies demonstrated a tight sorption of collagenase on collagen surfaces that follows a Freundlich sorption isotherm and results in a degradation constant of 3.8 × 10 mol/l for the minirods. The diffusion coefficients of FITC dextran 20 and 70 (3 × 10 and 2.4 × 10 cm/h) in water were analyzed by fluorescence correlation spectroscopy (FCS). Using these data, the mathematical model was verified by two-dimensional simulations. The numerical results agreed well with the measurements. © 2007 Elsevier B.V. All rights reserved.}, author = {Metzmacher, Iris and Radu, Adrian Florin and Bause, Markus and Knabner, Peter and Friess, Wolfgang}, doi = {10.1016/j.ejpb.2007.02.013}, faupublication = {yes}, journal = {European Journal of Pharmaceutics and Biopharmaceutics}, keywords = {Collagen; Enzymatic adsorption; Enzymatic degradation; FCS; Mathematical model; Numerical simulation}, pages = {349-360}, peerreviewed = {Yes}, title = {{A} model describing the effect of enzymatic degradation on drug release from collagen minirods}, volume = {67}, year = {2007} } @article{faucris.205333830, abstract = {The aim of this paper is to derive and analyze a variational model for the joint estimation of motion and reconstruction of image sequences, which is based on a time-continuous Eulerian motion model. The model can be set up in terms of the continuity equation or the brightness constancy equation. The analysis in this paper focuses on the latter for robust motion estimation on sequences of twodimensional images. We rigorously prove the existence of a minimizer in a suitable function space setting. Moreover, we discuss the numerical solution of the model based on primal-dual algorithms and investigate several examples. Finally, the benefits of our model compared to existing techniques, such as sequential image reconstruction and motion estimation, are shown.}, author = {Burger, Martin and et al.}, author_hint = {Burger M, Dirks H, Schonlieb CB}, doi = {10.1137/16M1084183}, faupublication = {no}, journal = {Siam Journal on Imaging Sciences}, keywords = {dynamic image reconstruction;motion estimation;image denoising;joint variational model;regularization;Eulerian motion model}, month = {Jan}, pages = {94-128}, peerreviewed = {Yes}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{A} {Variational} {Model} for {Joint} {Motion} {Estimation} and {Image} {Reconstruction}}, url = {https://arxiv.org/pdf/1607.03255}, volume = {11}, year = {2018} } @article{faucris.117783644, author = {Knabner, Peter and Tapp, Christoph and Thiele, Kathrin}, doi = {10.1016/S1464-1909(01)00013-2}, faupublication = {yes}, journal = {Physics and Chemistry of the Earth, Part B}, pages = {319-324}, peerreviewed = {Yes}, title = {{Adaptivity} in the finite volume discretization of variable density flows in porous media}, volume = {26}, year = {2001} } @article{faucris.204938499, abstract = {This paper presents an a priori error analysis of a fully discrete scheme for the numerical solution of the transient, nonlinear Darcy-Nernst-Planck-Poisson system. The scheme uses the second order backward difference formula (BDF2) in time and the mixed finite element method with Raviart-Thomas elements in space. In the first step, we show that the solution of the underlying weak continuous problem is also a solution of a third problem for which an existence result is already established. Thereby a stability estimate arises, which provides an L-∞ bound of the concentrations / masses of the system. This bound is used as a level for a cut-off operator that enables a proper formulation of the fully discrete scheme. The error analysis works without semi-discrete intermediate formulations and reveals convergence rates of optimal orders in time and space. Numerical simulations validate the theoretical results for lowest order finite element spaces in two dimensions.}, author = {Frank, Florian and Knabner, Peter}, doi = {10.1051/m2an/2017002}, faupublication = {yes}, journal = {Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique}, keywords = {Stokes / Darcy-Nernst-Planck-Poisson system;mixed finite elements;backward difference formula;error analysis;porous media}, pages = {1883-1902}, peerreviewed = {Yes}, title = {{Convergence} analysis of a {BDF2}/mixed finite element discretization of a {Darcy}–{Nernst}–{Planck}–{Poisson} system}, volume = {51}, year = {2017} } @article{faucris.106933024, abstract = {

Based on the local discontinuous Galerkin method, two substantially different mixed formulations for the subjective surfaces problem are compared using a number of numerical tests of various types. The work also performs the energy stability analysis for both schemes.},
author = {Fried, Michael and Aizinger, Vadym and Bungert, Leon},
doi = {10.1007/s00791-018-0291-4},
faupublication = {yes},
journal = {Computing and Visualization in Science},
keywords = {Local discontinuous Galerkin method; Image segmentation; Subjective surfaces; Stability analysis; Mixed formulation; Divergence form; Edge detection},
peerreviewed = {Yes},
title = {{Comparison} of two local discontinuous {Galerkin} formulations for the subjective surfaces problem},
url = {https://link.springer.com/article/10.1007%2Fs00791-018-0291-4},
year = {2018}
}
@article{faucris.117782764,
abstract = {Solute transport through heterogeneous porous media considered in environmental and industrial problems is often characterized by high Péclet numbers. In this paper we develop a new numerical approach to advection-dominated transport consisting of coupling an accurate mass-conservative mixed finite element method (MFEM), used to solve Darcy flows, with a particle method, stable and free of numerical diffusion, for non-reactive transport simulations. The latter is the efficient global random walk (GRW) algorithm, which performs the simultaneous tracking of arbitrarily large collections of particles on regular lattices at computational costs comparable to those of single-trajectory simulations using traditional particle tracking (PT). MFEM saturated flow solutions are computed for spatially heterogeneous hydraulic conductivities parameterized as samples of random fields. The coupling is achieved by projecting the velocity field from the MFEM basis onto the regular GRW lattice. Preliminary results show that MFEM-GRW is tens of times faster than the full MFEM flow and transport simulation. © 2012.},
author = {Suciu, Nicolae and Radu, Adrian Florin and Prechtel, Alexander and Brunner, Fabian and Knabner, Peter},
doi = {10.1016/j.cam.2012.06.027},
faupublication = {yes},
journal = {Journal of Computational and Applied Mathematics},
keywords = {Advection-dominated transport; Porous media; Random walk methods},
pages = {27-37},
peerreviewed = {Yes},
title = {{A} coupled finite element-global random walk approach to advection-dominated transport in porous media with random hydraulic conductivity},
volume = {246},
year = {2013}
}
@article{faucris.205334362,
abstract = {The goal of dynamic magnetic resonance imaging (dynamic MRI) is to visualize tissue properties and their local changes over time that are traceable in the MR signal. We propose a new variational approach for the reconstruction of subsampled dynamic MR data, which combines smooth, temporal regularization with spatial total variation regularization. In particular, it furthermore uses the infimal convolution of two total variation Bregman distances to incorporate structural a priori information from an anatomical MRI prescan into the reconstruction of the dynamic image sequence. The method promotes the reconstructed image sequence to have a high structural similarity to the anatomical prior, while still allowing for local intensity changes which are smooth in time. The approach is evaluated using artificial data simulating functional magnetic resonance imaging (fMRI), and experimental dynamic contrast-enhanced magnetic resonance data from small animal imaging using radial golden angle sampling of the k-space.},
author = {Burger, Martin and et al.},
author_hint = {Rasch J, Kolehmainen V, Nivajarvi R, Kettunen M, Grohn O, Burger M, Brinkmann EM},
doi = {10.1088/1361-6420/aac3af},
faupublication = {no},
journal = {Inverse Problems},
keywords = {dynamic magnetic resonance imaging;spatio-temporal regularization;structural prior;infimal convolution of Bregman distances;total variation;golden angle subsampling},
peerreviewed = {Yes},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{Dynamic} {MRI} reconstruction from undersampled data with an anatomical prescan},
url = {https://arxiv.org/pdf/1712.00099.pdf},
volume = {34},
year = {2018}
}
@article{faucris.214175734,
abstract = {Second and higher order numerical approximations of conservation laws for vector fields call for the use of limiting techniques based on generalized monotonicity criteria. In this paper, we introduce a family of directional vertex-based slope limiters for tensorvalued gradients of formally second-order accurate piecewise-linear discontinuous Galerkin (DG) discretizations. The proposed methodology enforces local maximum principles for scalar products corresponding to projections of a vector field onto the unit vectors of a frame-invariant orthogonal basis. In particular, we consider anisotropic limiters based on singular value decompositions and the Gram-Schmidt orthogonalization procedure. The proposed extension to hyperbolic systems features a sequential limiting strategy and a global invariant domain fix. The pros and cons of different approaches to vector limiting are illustrated by the results of numerical studies for the two-dimensional shallow water equations and for the Euler equations of gas dynamics. (C) 2019 Elsevier Inc. All rights reserved.},
author = {Hajduk, Hennes and Kuzmin, Dmitri and Aizinger, Vadym},
doi = {10.1016/j.jcp.2019.01.032},
faupublication = {yes},
journal = {Journal of Computational Physics},
note = {CRIS-Team WoS Importer:2019-03-22},
pages = {308-325},
peerreviewed = {Yes},
title = {{New} directional vector limiters for discontinuous {Galerkin} methods},
volume = {384},
year = {2019}
}
@article{faucris.123846404,
abstract = {Biodegradable collagen matrices have become a promising alternative to traditional drug delivery systems. The relevant mechanisms in controlled drug release are the diffusion of water into the collagen matrix, the swelling of the matrix coming along with drug release, and enzymatic degradation of the matrix with additional simultaneous drug release. These phenomena have been extensively studied in the past experimentally, via numerical simulations as well as analytically. However, a rigorous derivation of the macroscopic model description, which includes the evolving microstructure due to the degradation process, is still lacking. Since matrix degradation leads to the release of physically entrapped active agent, a good understanding of these phenomena is very important. We present such a derivation using formal twoscale asymptotic expansion in a level set framework and complete our results with numerical simulations in comparison with experimental data. Biodegradable collagen matrices have become a~promising alternative to traditional drug delivery systems. The relevant mechanisms in controlled drug release are the diffusion of water into the collagen matrix, the swelling of the matrix coming along with drug release, and enzymatic degradation of the matrix with additional simultaneous drug release. These phenomena have been extensively studied in the past experimentally, via numerical simulations as well as analytically. However, a rigorous derivation of the macroscopic model description, which includes the evolving microstructure due to the degradation process, is still lacking. Since matrix degradation leads to the release of physically entrapped active agent, a~good understanding of these phenomena is very important. The authors present such a~derivation using formal twoscale asymptotic expansion in a~level set framework and complete their results with numerical simulations in comparison with experimental data. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.},
author = {Ray, Nadja and van Noorden, Tycho and Radu, Adrian Florin and Friess, Wolfgang and Knabner, Peter},
doi = {10.1002/zamm.201200196},
faupublication = {yes},
journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik},
keywords = {Drug release; Evolving microstructure; Homogenization; Mixed finite element method; Numerical simulation; Porous media},
pages = {811-822},
peerreviewed = {Yes},
title = {{Drug} release from collagen matrices including an evolving microstructure},
volume = {93},
year = {2013}
}
@incollection{faucris.117982084,
abstract = {Contaminants with very low water solubilities (e.g. polycyclic aromatic hydrocarbons) play an important role in risk assessment of dangerous wastes and development of soil remediation. The mobility of such hydrophobic substances can be strongly affected by the existence of carriers (e.g. dissolved organic carbon), which can adsorb the contaminant and thereby enhance or reduce its velocity. The numerical simulation of the spreading of these contaminants, requires the solution of reactive transport equations for all involved components, coupled by the contaminant’s sorption to the carrier. Our development is based on a model [2], in which all the carrier’s influence on the contaminant transport is contained in an effective adsorption isotherm, depending on the carrier concentration and thereby also on space and time. First we shortly summarize the modelling of reactive transport of a single component (carrier, contaminant, carrier bound contaminant) in a porous medium, then in section 3 we combine the two equations for the contaminant components. The properties of the contaminant’s effective isotherm and its influence on the transport equation are discussed in section 4.},
address = {Berlin, Heidelberg},
author = {Knabner, Peter and Schneid, Eckhard},
booktitle = {Scientific Computing in Chemical Engineering},
doi = {10.1007/978-3-642-80149-5_14},
editor = {Frerich Keil, Wolfgang Mackens, Heinrich Voß, Joachim Werther},
faupublication = {yes},
isbn = {978-3-642-80151-8},
pages = {129-135},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Qualitative} {Properties} of a {Model} for {Carrier} {Facilitated} {Groundwater} {Contaminant} {Transport}},
url = {http://link.springer.com/chapter/10.1007%2F978-3-642-80149-5_14},
year = {1996}
}
@article{faucris.117797504,
author = {Knabner, Peter and Otto, Felix},
doi = {10.1016/S0362-546X(98)00352-6},
faupublication = {yes},
journal = {Nonlinear Analysis - Theory Methods & Applications},
keywords = {Degenerate parabolic systems; Flow and transport in porous media; Stability; Uniqueness},
pages = {381-403},
peerreviewed = {Yes},
title = {{Solute} transport in porous media with equilibrium and nonequilibrium multiple-site adsorption: {Uniqueness} of weak solutions},
volume = {42},
year = {2000}
}
@article{faucris.116659884,
author = {Vibe, Alexander and Marheineke, Nicole},
doi = {10.1080/23324309.2016.1181090},
faupublication = {yes},
journal = {Journal of Computational and Theoretical Transport},
peerreviewed = {Yes},
title = {{Impact} of weak particle inertia on dilute suspensions of ellipsoids},
year = {2016}
}
@article{faucris.121082104,
abstract = {We present a cross-platform scaling investigation for an OpenMP parallelization of UTBEST3D – a coastal and regional ocean code based on the discontinuous Galerkin finite element method. The study is conducted for a real life application on an unstructured computational mesh of the Northwest Atlantic with realistic topography and well resolved coast line on a broad selection of current computing platforms. Four numerical setups of increasing physical and computational complexity are used for comparison: barotropic with no vertical eddy viscosity, barotropic with an algebraic eddy viscosity parametrization, baroclinic with an algebraic eddy viscosity, and baroclinic with *k *– vertical turbulence closure. In addition to Intel Xeon and IBM Power6/PowerPC architectures, we also include Intel’s new MIC processor Xeon Phi in the evaluation. Good scalability is found across all platforms with Intel Xeon CPUs producing the best runtime results and Xeon Phi demonstrating the best parallel efficiency.},
author = {Reuter, Balthasar and Aizinger, Vadym and Köstler, Harald},
doi = {10.1016/j.compfluid.2015.05.020},
faupublication = {yes},
journal = {Computers & Fluids},
keywords = {Discontinuous Galerkin finite element method; 3D shallow water equations; OpenMP; Intel Xeon Phi; IBM PowerPC; IBM Power6},
pages = {325 - 335},
peerreviewed = {Yes},
title = {{A} multi-platform scaling study for an {OpenMP} parallelization of a discontinuous {Galerkin} ocean model},
url = {http://www.sciencedirect.com/science/article/pii/S0045793015001759},
volume = {117},
year = {2015}
}
@unpublished{faucris.216545688,
abstract = {The aim of this paper is to further develop mathematical models for bleb
formation in cells, including cell-membrane interactions with linker proteins.
This leads to nonlinear reaction-diffusion equations on a surface coupled to
fluid dynamics in the bulk. We provide a detailed mathematical analysis and
investigate some singular limits of the model, connecting it to previous
literature. Moreover, we provide numerical simulations in different scenarios,
confirming that the model can reproduce experimental results on bleb initation.},
author = {Werner, Philipp and Burger, Martin and Pietschmann, Jan-Frederik},
faupublication = {yes},
keywords = {Cell blebbing, Surface PDEs, Fluid-Structure Interaction, Free Boundary Problems},
note = {https://cris.fau.de/converis/publicweb/Publication/216545688},
peerreviewed = {automatic},
title = {{A} {PDE} model for bleb formation and interaction with linker proteins},
url = {https://arxiv.org/abs/1904.03474},
year = {2019}
}
@article{faucris.207466853,
author = {Burger, Martin and et al.},
author_hint = {Burger M, Hausser F, Stöcker C, Voigt A},
doi = {10.1016/j.jcp.2006.11.026},
faupublication = {no},
journal = {Journal of Computational Physics},
note = {WWU::5575},
pages = {183-205},
peerreviewed = {No},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{A} level set approach to anisotropic flows with curvature regularization},
volume = {225},
year = {2007}
}
@article{faucris.211596795,
abstract = {In this paper, we derive a theoretical analysis of nonsymmetric interior penalty discontinuous Galerkin methods for solving the Cahn–Hilliard equation. We prove unconditional unique solvability of the discrete system and derive stability bounds with a generalized chemical energy density. Convergence of the method is obtained by optimal a priori error estimates. Our analysis is valid for both symmetric and nonsymmetric versions of the discontinuous Galerkin formulation.

}, author = {Liu, Chen and Frank, Florian and Rivière, Béatrice}, doi = {10.1002/num.22362}, faupublication = {yes}, journal = {Numerical Methods For Partial Differential Equations}, keywords = {Cahn–Hilliard equation; error analysis; interior penalty discontinuous Galerkin methods; stability analysis; unique solvability}, month = {Jan}, peerreviewed = {Yes}, title = {{Numerical} error analysis for nonsymmetric interior penalty discontinuous {Galerkin} method of {Cahn}–{Hilliard} equation}, year = {2019} } @article{faucris.201552267, abstract = {

In this paper, we derive mathematical models for the dynamics of superparamagnetic nanoparticles under the influence of applied magnetic fields. Such models are needed in many applications, e.g. magnetic drug targeting in cancer therapy. They are the starting point for the development of stable numerical approaches and for the formulation of optimization problems, which are needed for the optimal design of magnetic field configurations. Furthermore, we show the existence and uniqueness of classical radially symmetrical solutions and illustrate their qualitative behaviour by numerical simulations using Matlab.

model for two-phase flow of incompressible fluids with dissolved noninteracting

polymers. The polymers are modeled by dumbbells subjected to general elastic springforce

potentials including in particular Hookean and finitely extensible, nonlinear elastic

(FENE) potentials. Their density and orientation are described by a Fokker-Planck-type

equation which is coupled to a Cahn-Hilliard and a momentum equation for phase-field

and gross velocity/pressure. Henry-type energy functionals are used to describe different

solubility properties of the polymers in the different phases or at the liquid-liquid interface.

Taking advantage of the underlying energetic/entropic structure of the system, we

prove existence of a weak solution globally in time for the case of FENE-potentials. As

a by-product in the case of Hookean spring potentials, we derive a macroscopic diffuse interface

model for two-phase flow of Oldroyd-B-type liquids.}, author = {Grün, Günther and Metzger, Stefan}, doi = {10.1142/S0218202516500196}, faupublication = {yes}, journal = {Mathematical Models & Methods in Applied Sciences}, pages = {823-866}, peerreviewed = {Yes}, title = {{On} micro-macro-models for two-phase flow with dilute polymeric solutions -- modeling and analysis}, volume = {26}, year = {2016} } @incollection{faucris.116676164, author = {Rivero-Rodriguez, Javier and Arne, Walter and Marheineke, Nicole and Wegener, Raimund and Pérez-Saborid, Miguel}, booktitle = {Progress in Industrial Mathematics at ECMI 2014}, faupublication = {yes}, peerreviewed = {unknown}, publisher = {Springer}, title = {{Setup} of viscous {Cosserat} rod model desribing electrospinning}, year = {2016} } @incollection{faucris.122038884, author = {Marheineke, Nicole and Wegener, Raimund}, booktitle = {Progress in Industrial Mathematics at ECMI 2010}, editor = {M. Günther, A. Bartel, M. Brunk, S. Schöps, M. Striebel}, faupublication = {yes}, pages = {239-246}, peerreviewed = {unknown}, publisher = {Springer}, title = {{Stochastic} {PDAE}-models and associated {Monte}-{Carlo} simulations for elastic threads in turbulent flows}, year = {2012} } @article{faucris.117796404, abstract = {We analyze a discretization method for a class of degenerate parabolic problems that includes the Richards' equation. This analysis applies to the pressure-based formulation and considers both variably and fully saturated regimes. To overcome the difficulties posed by the lack in regularity, we first apply the Kirchhoff transformation and then integrate the resulting equation in time. We state a conformal and a mixed variational formulation and prove their equivalence. This will be the underlying idea of our technique to get error estimates. A regularization approach is combined with the Euler implicit scheme to achieve the time discretization. Again, equivalence between the two formulations is demonstrated for the semidiscrete case. The lowest order Raviart-Thomas mixed finite elements are employed for the discretization in space. Error estimates are obtained, showing that the scheme is convergent. © 2004 Society for Industrial and Applied Mathematics.}, author = {Radu, Adrian Florin and Pop, Iuliu Sorin and Knabner, Peter}, doi = {10.1137/S0036142902405229}, faupublication = {yes}, journal = {SIAM Journal on Numerical Analysis}, keywords = {De-generate parabolic problems; Error estimates; Euler implicit scheme; Mixed finite elements; Porous media; Regularization; Richards' equation}, pages = {1452-1478}, peerreviewed = {Yes}, title = {{Order} of convergence estimates for an {Euler} implicit, mixed finite element discretization of {Richards}' equation}, volume = {42}, year = {2004} } @article{faucris.113569984, author = {Grün, Günther and Abels, Helmut and Garcke, Harald}, faupublication = {yes}, journal = {Mathematical Models & Methods in Applied Sciences}, pages = {1150013-1150052}, peerreviewed = {Yes}, title = {{Thermodynamically} consistent diffuse interface models for incompressible two-phase flows with different densities}, volume = {22}, year = {2012} } @article{faucris.116639644, abstract = {We present and investigate techniques for optimizing particle dispersions in all kinds of Reynolds number flows. In particular, we show the range of application, power and efficiency of space mapping approaches that are based on a hierarchy of models ranging from a complex (fine, accurate, costly) to simple (coarse, rough, cheap) model. Space mapping turns out to be a reasonable approximation to optimal control and a competitive alternative to instantaneous control regarding speed and memory demands when dealing with complex, non-stationary problems. Moreover it allows the easy and efficient treatment of stochastic design problems. To control random particle dynamics in a turbulent flow, we suggest a Monte-Carlo aggressive space mapping algorithm which yields very convincing numerical results. © 2011 Springer Science+Business Media, LLC.}, author = {Marheineke, Nicole and Pinnau, René and Reséndiz, Edgar}, doi = {10.1007/s11081-011-9150-6}, faupublication = {yes}, journal = {Optimization and Engineering}, keywords = {Instantaneous control; k-ε{lunate} turbulence model; Navier-Stokes equations; Optimal control; Particle dynamics; Space mapping technique; Stochastic control; Tracking problem}, pages = {101-120}, peerreviewed = {Yes}, title = {{Space} mapping-focused control techniques for particle dispersions in fluids}, volume = {13}, year = {2012} } @article{faucris.119186584, abstract = {A multi-level method for the determination of nonlinear coefficient functions of parabolic partial differential equations is presented as an example of the reconstruction of the hydraulic properties of porous media from soil column outflow experiments. A linear stability and error analysis is used to characterize the ill-posedness of the inverse problem. Founded on this analysis, optimal experimental design problems can be formulated. Numerical examples are presented which show that the method described leads to a stable solution of the inverse problem.}, author = {Bitterlich, Sandro and Knabner, Peter}, doi = {10.1088/0266-5611/19/5/302}, faupublication = {yes}, journal = {Inverse Problems}, pages = {1011-1030}, peerreviewed = {Yes}, title = {{Experimental} design for outflow experiments based on a multi-level identification method for material laws}, volume = {19}, year = {2003} } @article{faucris.216729740, author = {Grün, Günther and Grillmeier, Hubertus}, doi = {10.1090/mcom/3372}, faupublication = {yes}, journal = {Mathematics of Computation}, pages = {1021-1059}, peerreviewed = {Yes}, title = {{Nonnegativity} preserving convergent schemes for the stochastic porous-medium equation}, year = {2018} } @inproceedings{faucris.208634631, abstract = {The accurate simulation of realistic flow scenarios is still a challenging problem, and a final answer has not yet been found. Nevertheless, flow simulations are nowadays ubiquitous during the design process of vehicles like aircrafts or cars, as well as in many other fields of science and engineering. Ideally such simulations should run in real-time and should be easily available to everyone. We have started to work in that direction last year when setting up an interactive web application for calculating the flow around a two-dimensional user-drawn airfoil using the finite element library Femlisp (http://www.femlisp.org).

The

conjugate gradient boundary iteration

(CGBI) is a domain decom-

position method for elliptic partial differential equations [1] [2] [3] [6

] [7].

In the context of fractional step methods [10], a Navier-Stokes solver based

on CGBI and a characteristic’s method was constructed. In this article,

numerical results for the incompressible flow past a backward facing step

and past a cylinder (both modelled in 2d) are presented.

},
author = {Kräutle, Serge and Wielage, Kerstin},
booktitle = {The Navier-Stokes Equations: Theory and Numerical Methods},
editor = {Rodolfo Salvi},
faupublication = {no},
isbn = {9780824706722},
pages = {247-255},
peerreviewed = {unknown},
series = {Lecture Notes in Pure and Applied Mathematics},
title = {{Numerical} results for the {CGBI} method to viscous channel flow},
volume = {223},
year = {2001}
}
@article{faucris.116634144,
abstract = {The space mapping technique aims at an efficient optimization of complex technical problems. Its success relies on the quality of the coarse model that might be deduced from either physical, algebraic or grid-based hierarchies of models. In this paper we perform a feasibility study for transport processes coming from the fields of fluid dynamics, semiconductors and radiation. We present appropriate model hierarchies and discuss the numerical performance. Space mapping shows to give very convincing suboptimal solutions to the actual fine model optimization regarding the balance of computational effort (speed and memory) and accuracy. © 2012 - IOS Press and the authors. All rights reserved.},
author = {Marheineke, Nicole and Pinnau, René},
doi = {10.3233/JCM-2012-0404},
faupublication = {yes},
journal = {Journal of Computational Methods in Sciences and Engineering},
keywords = {Aggressive space mapping; flow control; optimal control; radiation optimization; semiconductor design},
pages = {63-74},
peerreviewed = {unknown},
title = {{Model} hierarchies in space-mapping optimization: {Feasibility} study for transport processes},
volume = {12},
year = {2012}
}
@article{faucris.204939039,
abstract = {This is the second in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source NIATLAB/GNU Octave toolbox. The intention of this ongoing project is to offer a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix/vector operations and is comprehensively documented. Particular attention was paid to maintaining a direct mapping between discretization terms and code routines as well as to supporting the full code functionality in GNU Octave. The present work focuses on a two-dimensional time dependent linear advection equation with space/time-varying coefficients, and provides a general order implementation of several slope limiting schemes for the DG method. (C) 2016 Elsevier Ltd. All rights reserved.},
author = {Reuter, Balthasar and Aizinger, Vadym and Wieland, Manuel and Frank, Florian and Knabner, Peter},
doi = {10.1016/j.camwa.2016.08.006},
faupublication = {yes},
journal = {Computers & Mathematics With Applications},
keywords = {Matlab/GNU Octave;Discontinuous Galerkin method;Slope limiting;Vectorization;Open source;Advection operator},
pages = {1896-1925},
peerreviewed = {Yes},
title = {{FESTUNG}: {A} {MATLAB}/{GNU} {Octave} toolbox for the discontinuous {Galerkin} method, {Part} {II}: {Advection} operator and slope limiting},
volume = {72},
year = {2016}
}
@article{faucris.205335160,
abstract = {Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses. In the last two decades interest has shifted from linear to nonlinear regularization methods, even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this shift towards modern nonlinear regularization methods, including their analysis, applications and issues for future research.In particular we will discuss variational methods and techniques derived from them, since they have attracted much recent interest and link to other fields, such as image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions and learning theory.},
author = {Burger, Martin and et al.},
author_hint = {Benning M, Burger M},
doi = {10.1017/S0962492918000016},
faupublication = {no},
journal = {Acta Numerica},
month = {Jan},
pages = {1-111},
peerreviewed = {unknown},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{Modern} regularization methods for inverse problems},
url = {https://arxiv.org/pdf/1801.09922.pdf},
volume = {27},
year = {2018}
}
@article{faucris.123947384,
author = {Grün, Günther},
faupublication = {no},
journal = {Mathematics of Computation},
pages = {1251-1279},
peerreviewed = {Yes},
title = {{On} the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions},
volume = {72},
year = {2003}
}
@article{faucris.123981484,
abstract = {The spinning of slender viscous jets can be asymptotically described by one-dimensional models that consist of systems of partial and ordinary differential equations. Whereas well-established string models only possess solutions for certain choices of parameters and configurations, the more sophisticated rod model is not limited by restrictions. It can be considered as an ε-regularized string model, but containing the slenderness ratio ε in the equations complicates its numerical treatment. We develop numerical schemes for fixed or enlarging (time-dependent) domains, using a finite volume approach in space with mixed central, up- and down-winded differences and stiffly accurate Radau methods for the time integration. For the first time, results of instationary simulations for a fixed or growing jet in a rotational spinning process are presented for arbitrary parameter ranges.},
author = {Arne, Walter and Marheineke, Nicole and Meister, Andreas and Schiessl, Stefan and Wegener, Raimund},
doi = {10.1016/j.jcp.2015.03.042},
faupublication = {yes},
journal = {Journal of Computational Physics},
keywords = {Finite volume scheme; Partial differential algebraic equations; Quaternions; Rotational spinning process; Special cosserat theory; Viscous fiber},
pages = {20-37},
peerreviewed = {unknown},
title = {{Finite} volume approach for the instationary {Cosserat} rod model describing the spinning of viscous jets},
volume = {294},
year = {2015}
}
@inproceedings{faucris.208634059,
author = {Neuß, Nicolas and Heisig, Marco},
booktitle = {Proceedings of the ELS 2016},
date = {2016-05-09/2016-05-10},
editor = {EPITA},
faupublication = {yes},
pages = {101-102},
peerreviewed = {Yes},
title = {{Distributed} {High} {Performance} {Computing} in {Common} {Lisp}},
url = {https://european-lisp-symposium.org/static/proceedings/2016.pdf},
venue = {Krakow},
year = {2016}
}
@article{faucris.119230144,
abstract = {This work deals with the optimal control of a fre e surface Stokes flow which responds to an applied outer pressure. Typical applications are fiber spinning or thin film manufacturing. We present and discuss two adjoint-based optimization approaches that differ in the treatment of the free boundary as either a state or control variable. In both cases the free boundary is modeled as the graph of a function. The PDE-constrained optimization problems are numerically solved by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, where the gradient of the reduced cost function is expressed in terms of adjoint variables. Numerical results for both strategies are finally compared with respect to accuracy and efficiency. © 2011 Society for Industrial and Applied Mathematics.},
author = {Repke, Sabine and Marheineke, Nicole and Pinnau, René},
doi = {10.1137/100797953},
faupublication = {yes},
journal = {SIAM Journal on Applied Mathematics},
keywords = {Film casting process; Free surface stokes flow; Lagrange formalism; Optimal control; Thin films},
pages = {2168-2184},
peerreviewed = {Yes},
title = {{Two} adjoint-based optimization approaches for a free surface {Stokes} flow},
volume = {71},
year = {2011}
}
@article{faucris.123963004,
abstract = {In this paper we present a model for crystal dissolution in porous media and analyse travelling wave solutions of the ensuing equations for a one-dimensional flow situation. We demonstrate the structure of the waves and we prove existence and uniqueness. The travelling wave description is characterized by a rate parameter k and a diffusion/dispersion parameter D. We investigate the limit processes as k→∞and D→0 and we obtain expressions for the rate of convergence. We also present some numerical results.},
author = {Van Duijn, C. J. (Hans) and Knabner, Peter},
faupublication = {yes},
journal = {European Journal of Applied Mathematics},
pages = {49-72},
peerreviewed = {Yes},
title = {{Travelling} wave behaviour of crystal dissolution in porous media flow},
volume = {8},
year = {1997}
}
@article{faucris.106871644,
author = {Grün, Günther and Becker, Jürgen and Blossey, Ralf and Neto, Chiara and Jacobs, Karin and Seemann, Ralf},
faupublication = {no},
journal = {Journal of Physics: Condensed Matter},
pages = {3355-3366},
peerreviewed = {Yes},
title = {{Satellite} hole formation during dewetting; experiment and simulation},
volume = {15},
year = {2003}
}
@article{faucris.113571964,
author = {Grün, Günther and Becker, Jürgen},
doi = {10.1088/0953-8984/17/9/002},
faupublication = {no},
journal = {Journal of Physics: Condensed Matter},
pages = {291-307},
peerreviewed = {unknown},
title = {{The} thin-film equation: recent advances and some new perspectives},
volume = {17},
year = {2005}
}
@article{faucris.122619464,
abstract = {We present a mass conservative finite element approach of second order accuracy for the numerical approximation of reactive solute transport in porous media modeled by a coupled system of advection-diffusion-reaction equations. The lowest order Brezzi-Douglas-Marini (BDM ) mixed finite element method is used. A modification based on the hybrid form of the approach is suggested for the discretization of the advective term. It is demonstrated numerically that this leads to optimal second order convergence of the flux variable. The modification improves the convergence behavior of the classical BDM scheme, which is known to be suboptimal of first order accuracy only for advection-diffusion problems; cf. [8]. Moreover, the new scheme shows more robustness for high Péclet numbers than the classical approach. A comparison with the Raviart-Thomas element (RT ) of second order accuracy for the approximation of the flux variable is also presented. For the case of strongly advection-dominated problems we propose a full upwind scheme. Various numerical studies, including also a nonlinear test problem, are presented to illustrate the numerical performance properties of the considered numerical methods. © 2011 Elsevier Ltd.},
author = {Brunner, Fabian and Radu, Adrian Florin and Bause, Markus and Knabner, Peter},
doi = {10.1016/j.advwatres.2011.10.001},
faupublication = {yes},
journal = {Advances in Water Resources},
keywords = {Mixed finite element methods; Optimal order convergence; Reactive transport},
pages = {163-171},
peerreviewed = {Yes},
title = {{Optimal} order convergence of a modified {BDM} 1 mixed finite element scheme for reactive transport in porous media},
volume = {35},
year = {2012}
}
@article{faucris.123847944,
abstract = {The semismooth Newton method was introduced in a paper by Qi and Sun (Math. Program. 58:353-367, 1993) and the subsequent work by Qi (Math. Oper. Res. 18:227-244, 1993). This method became the basis of many solvers for certain classes of nonlinear systems of equations defined by a nonsmooth mapping. Here we consider a particular system of equations that arises from the discretization of a reactive transport model in the subsurface including mineral precipitation-dissolution reactions. The model is highly complicated and uses a coupling of PDEs, ODEs, and algebraic equations, together with some complementarity conditions arising from the equilibrium conditions of the minerals. The aim is to show that this system, though quite complicated, usually satisfies the convergence criteria for the semismooth Newton method, and can therefore be solved by a locally quadratically convergent method. This gives a theoretical sound approach for the solution of this kind of applications, whereas the geoscientists community most frequently applies algorithms involving some kind of trial-and-error strategies. © 2010 Springer Science+Business Media, LLC.},
author = {Buchholzer, Hannes and Kanzow, Christian and Knabner, Peter and Kräutle, Serge},
doi = {10.1007/s10589-010-9379-6},
faupublication = {yes},
journal = {Computational Optimization and Applications},
keywords = {Complementarity problems; Mineral precipitation-dissolution; Quadratic convergence; Reactive transport; Semismooth Newton method},
pages = {193-221},
peerreviewed = {Yes},
title = {{The} semismooth {Newton} method for the solution of reactive transport problems including mineral precipitation-dissolution reactions},
volume = {50},
year = {2011}
}
@inproceedings{faucris.203704185,
address = {Colmar, Alsace, France},
author = {Schönwetter, Dominik and Ditter, Alexander and Kleinert, Bruno and Hendricks, Arne and Aizinger, Vadym and Köstler, Harald and Fey, Dietmar},
booktitle = {Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications},
date = {2015-07-21/2015-07-23},
doi = {10.5220/0005566603770382},
faupublication = {yes},
isbn = {978-989-758-120-5},
keywords = {Crisis modeling and simulation; Environmental modeling; Multiscale simulation},
note = {UnivIS-Import:2018-09-06:Pub.2015.tech.IMMD.IMMD3.tsunam},
pages = {377-382},
peerreviewed = {unknown},
publisher = {SciTePress},
title = {{Tsunami} and {Storm} {Surge} {Simulation} {Using} {Low} {Power} {Architectures} - {Concept} and {Evaluation}},
venue = {Colmar},
year = {2015}
}
@article{faucris.208179475,
abstract = {Advances in pore-scale imaging (e.g., μ-CT scanning), increasing availability of computational resources, and recent developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multi-phase flow on pore structures feasible. Quasi-static methods, where the viscous and the capillary limit are iterated sequentially, fall short in rigorously capturing crucial flow phenomena at the pore scale. Direct simulation techniques are needed that account for the full coupling between capillary and viscous flow phenomena. Consequently, there is a strong demand for robust and effective numerical methods that can deliver high-accuracy, high-resolution solutions of pore-scale flow in a computationally efficient manner. Direct simulations of pore-scale flow on imaged volumes can yield important insights about physical phenomena taking place during multi-phase, multi-component displacements. Such simulations can be utilized for optimizing various enhanced oil recovery (EOR) schemes and permit the computation of effective properties for Darcy-scale multi-phase flows.We implement a phase-field model for the direct pore-scale simulation of incompressible flow of two immiscible fluids. The model naturally lends itself to the transport of fluids with large density and viscosity ratios. In the phase-field approach, the fluid-phase interfaces are expressed in terms of thin transition regions, the so-called diffuse interfaces, for increased computational efficiency. The conservation law of mass for binary mixtures leads to the advective Cahn–Hilliard equation and the condition that the velocity field is divergence free. Momentum balance, on the other hand, leads to the Navier–Stokes equations for Newtonian fluids modified for two-phase flow and coupled to the advective Cahn–Hilliard equation. Unlike the volume of fluid (VoF) and level-set methods, which rely on regularization techniques to describe the phase interfaces, the phase-field method facilitates a thermodynamic treatment of the phase interfaces, rendering it more physically consistent for the direct simulations of two-phase pore-scale flow. A novel geometric wetting (wall) boundary condition is implemented as part of the phase-field method for the simulation of two-fluid flows with moving contact lines. The geometric boundary condition accurately replicates the prescribed equilibrium contact angle and is extended to account for dynamic (non-equilibrium) effects. The coupled advective Cahn–Hilliard and modified Navier–Stokes (phase-field) system is solved by using a robust and accurate semi-implicit finite volume method. An extension of the momentum balance equations is also implemented for Herschel–Bulkley (non-Newtonian) fluids. Non-equilibrium-induced two-phase flow problems and dynamic two-phase flows in simple two-dimensional (2-D) and three-dimensional (3-D) geometries are investigated to validate the model and its numerical implementation. Quantitative comparisons are made for cases with analytical solutions. Two-phase flow in an idealized 2-D pore-scale conduit is simulated to demonstrate the viability of the proposed direct numerical simulation approac},
author = {Alpak, Faruk Omer and Rivière, Béatrice and Frank, Florian},
doi = {10.1007/s10596-015-9551-2},
faupublication = {no},
journal = {Computational Geosciences},
keywords = {phase-field method; two-phase flow; pore-scale flow simulation; CFD; digital rock; finite volume method; thermodynamics; contact line motion; dynamic contact angle; wetting},
pages = {881–908},
peerreviewed = {Yes},
title = {{A} phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition},
url = {https://link.springer.com/article/10.1007/s10596-015-9551-2},
volume = {20},
year = {2016}
}
@article{faucris.117922024,
abstract = {Transport processes in heterogeneous media such as ionized plasmas, natural porous media, and turbulent atmosphere are often modeled as diusion processes in random velocity elds. Using the Ito ̂ formalism, we decompose the second spatial moments of the concentration and the equivalent eective dispersion coecients in terms corresponding to various physical factors which in uence the transport. We explicitly dene \ergodic " dispersion coecients, independent of the initial conditions and completely determined by local disper-sion coecients and velocity correlations. Ergodic coecients govern an upscaled process which describes the transport at large tine-space scales. The non-ergodic behavior at nite times shown by numerical experiments for large initial plumes is explained by \memory terms " accounting for correlations between initial po-sitions and velocity uctuations on the trajectories of the solute molecules.},
author = {Suciu, Nicolae and Vamo̧s, Cǎlin and Vereecken, Harry and Sabelfeld, Karl and Knabner, Peter},
faupublication = {yes},
journal = {Revue d'Analyse Numérique et de Théorie de l'Approximation},
keywords = {second spatial moment; solute molecule; upscaled process; memory term; ergodic dispersion coecients; nite time; heterogeneous medium; initial positions; ito formalism; ergodic coecients; non-ergodic behavior; large tine-space scale; velocity correlation; equivalent eective dispersion; coecients; initial condition; natural porous medium; large initial plume; various physical factor; local disper-sion coecients; numerical experiment; turbulent atmosphere; random velocity eld; velocity uctuations; ionized plasma},
pages = {221-238},
peerreviewed = {Yes},
title = {{Ito} equation model for dispersion of solutes in heterogeneous media},
volume = {37},
year = {2008}
}
@article{faucris.204144387,
author = {Ray, Nadja and Rupp, Andreas and Schulz, Raphael and Knabner, Peter},
doi = {10.1007/s11242-018-1099-x},
faupublication = {yes},
journal = {Transport in Porous Media},
keywords = {Upscaling; Tortuosity; Diffusion in porous media},
pages = {803-824},
peerreviewed = {Yes},
title = {{Old} and {New} {Approaches} {Predicting} the {Diffusion} in {Porous} {Media}},
volume = {124},
year = {2018}
}
@article{faucris.117799044,
abstract = {We analyze mathematically and numerically a model derived in part 1 of this paper [Knabner et el, this issue]. The model deals with carrier- influenced transport and besides advective and dispersive transport and equilibrium and nonequilibrium sorption takes into account both carrier facilitation and cosorption. Guidelines are derived, whether the overall mobility is enhanced or reduced and various other properties of the model elucidated, in particular for varying carrier concentrations. We indicate how to modify existing numerical codes for the usual adsorption model and discuss simulations for experimental data sets.},
author = {Totsche, Kai Uwe and Knabner, Peter and Kögel-Knabner, Ingrid},
doi = {10.1029/95WR02993},
faupublication = {yes},
journal = {Water Resources Research},
pages = {1623-1634},
peerreviewed = {Yes},
title = {{The} modeling of reactive solute transport with sorption to mobile and immobile sorbents. 2. {Model} discussion and numerical simulation},
volume = {32},
year = {1996}
}
@article{faucris.212710190,
abstract = {The hepatitis C virus (HCV) RNA replication cycle is a dynamic intracellular process occurring in three-dimensional space (3D), which is difficult both to capture experimentally and to visualize conceptually. HCV-generated replication factories are housed within virus-induced intracellular structures termed membranous webs (MW), which are derived from the Endoplasmatic Reticulum (ER). Recently, we published 3D spatiotemporal resolved diffusion-reaction models of the HCV RNA replication cycle by means of surface partial differential equation (sPDE) descriptions. We distinguished between the basic components of the HCV RNA replication cycle, namely HCV RNA, non-structural viral proteins (NSPs), and a host factor. In particular, we evaluated the sPDE models upon realistic reconstructed intracellular compartments (ER/MW). In this paper, we propose a significant extension of the model based upon two additional parameters: different aggregate states of HCV RNA and NSPs, and population dynamics inspired diffusion and reaction coefficients instead of multilinear ones. The combination of both aspects enables realistic modeling of viral replication at all scales. Specifically, we describe a replication complex state consisting of HCV RNA together with a defined amount of NSPs. As a result of the combination of spatial resolution and different aggregate states, the new model mimics a cis requirement for HCV RNA replication. We used heuristic parameters for our simulations, which were run only on a subsection of the ER. Nevertheless, this was sufficient to allow the fitting of core aspects of virus reproduction, at least qualitatively. Our findings should help stimulate new model approaches and experimental directions for virology.},
author = {Knodel, Markus and Targett-Adams, Paul and Grillo, Alfio and Herrmann, Eva and Wittum, Gabriel},
doi = {10.3390/ijerph16030513},
faupublication = {yes},
journal = {International Journal of Environmental Research and Public Health},
note = {CRIS-Team WoS Importer:2019-03-08},
peerreviewed = {Yes},
title = {{Advanced} {Hepatitis} {C} {Virus} {Replication} {PDE} {Models} within a {Realistic} {Intracellular} {Geometric} {Environment}},
volume = {16},
year = {2019}
}
@incollection{faucris.206530022,
author = {Luckner, Thomas and Sommer, Thomas and Luckner, Ludwig and Bilek, Felix and Knabner, Peter and Prechtel, Alexander},
booktitle = {KORA - Synopse "Systemanalyse, Modellierung und Prognose der Wirkungen natürlicher Schadstoffminderungsprozesse - eine rezente Synopse"},
faupublication = {yes},
pages = {1-81},
peerreviewed = {unknown},
series = {Gemeinsame Mitteilungen des Dresdner Grundwasserforschungszentrum e.V. und seiner Partner},
title = {{Grundlagen} der {Systemanalyse}, {Modellierung} und {Prognose}},
volume = {5},
year = {2008}
}
@article{faucris.116658124,
author = {Grothaus, Martin and Marheineke, Nicole},
doi = {10.1093/imanum/drv056},
faupublication = {yes},
journal = {IMA Journal of Numerical Analysis},
peerreviewed = {Yes},
title = {{On} a nonlinear partial differential algebraic system arising in technical textile industry: {Analysis} and numerics},
year = {2015}
}
@article{faucris.109050744,
author = {Grün, Günther and Giacomelli, Lorenzo and Dal Passo, Roberta},
faupublication = {no},
journal = {Annali della Scuola Normale Superiore di Pisa-Classe di Scienze},
pages = {437-463},
peerreviewed = {Yes},
title = {{A} waiting time phenomenon for thin film equations},
volume = {XXX},
year = {2001}
}
@incollection{faucris.116454624,
address = {Heidelberg},
author = {Grün, Günther and Giacomelli, Lorenzo and Dal Passo, Roberta},
booktitle = {Geometric analysis and nonlinear partial differential equations},
editor = {S. Hildebrandt, H. Karcher},
faupublication = {no},
pages = {637-648},
peerreviewed = {unknown},
publisher = {Springer-Verlag},
title = {{Waiting} time phenomena for degenerate parabolic equations -- a unifying approach},
year = {2003}
}
@incollection{faucris.118046324,
address = {Dresden},
author = {Prechtel, Alexander and Hoffmann, Joachim and Kräutle, Serge and Knabner, Peter},
booktitle = {Modellierung und Prognose von Natural Attenuation-Prozessen im Untergrund},
faupublication = {yes},
pages = {75-90},
peerreviewed = {unknown},
series = {Gemeinsame Mitteilungen des Dresdner Grundwasserforschungszentrum e.V. und seiner Partner},
title = {{Reaktive} {Mehrkomponentenprobleme}: {Sicherung} von {Effizienz} und {Zuverlässigkeit}},
volume = {3},
year = {2006}
}
@article{faucris.204146417,
abstract = {The morphology of presynaptic specializations can vary greatly ranging from classical single-release-site boutons in the central nervous system to boutons of various sizes harboring multiple vesicle release sites. Multi-release-site boutons can be found in several neural contexts, for example at the neuromuscular junction (NMJ) of body wall muscles of Drosophila larvae. These NMJs are built by two motor neurons forming two types of glutamatergic multi-release-site boutons with two typical diameters. However, it is unknown why these distinct nerve terminal configurations are used on the same postsynaptic muscle fiber. To systematically dissect the biophysical properties of these boutons we developed a full three-dimensional model of such boutons, their release sites and transmitter-harboring vesicles and analyzed the local vesicle dynamics of various configurations during stimulation. Here we show that the rate of transmission of a bouton is primarily limited by diffusion-based vesicle movements and that the probability of vesicle release and the size of a bouton affect bouton-performance in distinct temporal domains allowing for an optimal transmission of the neural signals at different time scales. A comparison of our in silico simulations with in vivo recordings of the natural motor pattern of both neurons revealed that the bouton properties resemble a well-tuned cooperation of the parameters release probability and bouton size, enabling a reliable transmission of the prevailing firing-pattern at diffusion-limited boutons. Our findings indicate that the prevailing firing-pattern of a neuron may determine the physiological and morphological parameters required for its synaptic terminals.},
author = {Knodel, Markus and et al.},
author_hint = {Knodel MM, Geiger R, Ge L, Bucher D, Grillo A, Wittum G, Schuster CM, Queisser G},
doi = {10.3389/fncom.2014.00101},
faupublication = {no},
journal = {Frontiers in Computational Neuroscience},
keywords = {neuromuscular junction;boutons;modeling and simulation;structure-function relationships;morphology;firing pattern;adaption},
peerreviewed = {Yes},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{Synaptic} bouton properties are tuned to best fit the prevailing firing pattern},
volume = {8},
year = {2014}
}
@incollection{faucris.117981864,
abstract = {The underlying physical processes and their specific properties are discussed, yielding a model for the spread of hydrophobic contaminants, which allows for numerical simulation. In the case of convection dominance the contaminant transport is approximated by means of a Lagrange-Galerkin approach. A numerical scheme is presented for transport with equilibrium sorption. Nonlinear sorption isotherms are identified with soil column experiments. The efficiency of the identification algorithm is mainly determined by the choice of an appropiate initial value and the numerical scheme to compute the gradient.},
address = {Berlin, Heidelberg},
author = {Knabner, Peter and Igler, B. A. and Kappmeier, H. and Schneid, Eckhard and Hempfling, Rüdiger},
booktitle = {Mathematik Schlüsseltechnologie für die Zukunft},
doi = {10.1007/978-3-642-60550-5_20},
editor = {Karl-Heinz Hoffmann, Willi Jäger, Thomas Lohmann, Hermann Schunck},
faupublication = {yes},
pages = {231-241},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Trägerbeeinflußter} und lösungsvermittelter {Transport} von {Umweltchemikalien} in porösen {Medien}},
url = {http://link.springer.com/chapter/10.1007%2F978-3-642-60550-5_20},
year = {1997}
}
@incollection{faucris.122532124,
author = {Panda, Satyananda and Marheineke, Nicole and Wegener, Raimund},
booktitle = {Progress in Industrial Mathematics at ECMI 2006},
editor = {L. L. Bonilla, M. Moscoso, G. Platero, J. M. Vega},
faupublication = {no},
pages = {685-690},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Dynamics} of curved viscous fibers},
year = {2007}
}
@article{faucris.209915729,
author = {Brinkmann, Eva Maria and Brinkmann, Eva Maria and Burger, Martin and Grah, Joana Sarah},
doi = {10.1007/s10851-018-0861-6},
faupublication = {yes},
journal = {Journal of Mathematical Imaging and Vision},
keywords = {Denoising; Helmholtz decomposition; (Higher-order) total variation (TV) regularisation; Variational methods; Natural differential operators; Sparse regularisation},
peerreviewed = {Yes},
title = {{Unified} {Models} for {Second}-{Order} {TV}-{Type} {Regularisation} in {Imaging}: {A} {New} {Perspective} {Based} on {Vector} {Operators}},
url = {https://arxiv.org/pdf/1802.01895.pdf},
year = {2018}
}
@article{faucris.209240734,
author = {Reuter, Balthasar and Rupp, Andreas and Aizinger, Vadym and Knabner, Peter},
doi = {10.1016/j.camwa.2018.12.020},
faupublication = {yes},
journal = {Computers & Mathematics With Applications},
keywords = {Darcy flow; Coupled model; Hydrostatic equations; Discrete energy stability analysis; Three-dimensional shallow water equations with free surface; Local discontinuous Galerkin method},
pages = {2291-2309},
peerreviewed = {Yes},
title = {{Discontinuous} {Galerkin} method for coupling hydrostatic free surface flows to saturated subsurface systems},
volume = {77},
year = {2019}
}
@article{faucris.117794864,
abstract = {We consider charged transport within a porous medium, which at the pore scale can be described by the non-stationary Stokes-Nernst-Planck-Poisson (SNPP) system. We state three different homogenization results using the method of two-scale convergence. In addition to the averaged macroscopic equations, auxiliary cell problems are solved in order to provide closed-form expressions for effective coefficients. Our aim is to study numerically the convergence of the models for vanishing microstructure, i. e.; the behavior for ε → 0, where is the characteristic ratio between pore diameter and size of the porous medium. To this end, we propose a numerical scheme capable of solving the fully coupled microscopic SNPP system and also the corresponding averaged systems. The discretization is performed fully implicitly in time using mixed finite elements in two space dimensions. The averaged models are evaluated using simulation results and their approximation errors in terms of ε are estimated numerically. © 2013 Springer-Verlag Berlin Heidelberg.},
author = {Frank, Florian and Ray, Nadja and Knabner, Peter},
doi = {10.1007/s00791-013-0189-0},
faupublication = {yes},
journal = {Computing and Visualization in Science},
keywords = {Colloidal transport; Homogenization; Mixed finite elements; Numerical simulation; Porous media; Stokes/Darcy-Nernst- Planck-Poisson system; Two-scale convergence},
pages = {385-400},
peerreviewed = {unknown},
title = {{Numerical} investigation of homogenized {Stokes}-{Nernst}-{Planck}-{Poisson} systems},
volume = {14},
year = {2011}
}
@inproceedings{faucris.207760461,
author = {Burger, Martin and et al.},
author_hint = {Arning K, Burger M, Eisenberg B, Engl H, He L},
booktitle = {PAMM Special Issue: ICIAM 07},
doi = {10.1002/pamm.200700396},
faupublication = {no},
note = {WWU::69509},
pages = {1120801-1120802},
peerreviewed = {No},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{Inverse} problems related to ion channels},
year = {2008}
}
@masterthesis{faucris.216987080,
abstract = {Novel approaches for medical methods use Magnetic Nanoparticles (MNP) for the treatment process. These nanoparticles with a diameter of about 100nm can also be used for
imaging purposes. In Magnetorelaxometry Imaging (MRXI), magnetic nanoparticles
are exposed to an external magnetic field induced by coils outside the region of interest. This
causes a torque on the magnetization leading to an alignment of the MNPs. The overlay of
the magnetic field induced by each MNP itself can be measured using Superconducting
Quantum Interference Devices (SQUIDs). The corresponding mathematical operator that models the MRXI experiment is severely ill-posed and the corresponding inverse
problem of determining the particle distribution is difficult to solve directly. In the recent
literature only basic regularization techniques like Tikhonov regularization and Truncated Singular Value Decomposition were used to derive a reasonable solution. Using
first-order regularization techniques like the Alternating Direction Method of Multipliers (ADMM), it is possible to include a-priori knowledge about the anticipated solution.
In this work we derive a sophisticated mathematical model of the MRXI operator and compare the impact of different regularization techniques on the solution, in particular in the
case of noisy data, for various simulated settings.

The book includes contributions from leading figures in business, science and academia that promote the application of mathematics to industry and emphasize industrial sectors that offer the most exciting opportunities. The contributions reinforce the role of mathematics as being a catalyst for innovation as well as an overarching resource for industry and business.

The book features an accessible presentation of real-world problems in industry and finance, provides insight and tools for engineers and scientists who will help them to solve similar problems and offers modeling and simulation techniques that will provide mathematicians with a source of fresh ideas and inspiration.}, doi = {10.1007/978-3-319-05365-3}, edition = {1}, editor = {Fontes, Magnus and Günther, Michael and Marheineke, Nicole}, faupublication = {yes}, isbn = {978-3-319-05365-3}, peerreviewed = {automatic}, publisher = {Springer}, series = {The European Consortium for Mathematics in Industry}, title = {{Progress} in {Industrial} {Mathematics} at {ECMI} 2012}, volume = {19}, year = {2014} } @article{faucris.204938230, abstract = {We consider an energy-based boundary condition to impose an equilibrium wetting angle for the Cahn-Hilliard-Navier-Stokes phase-field model on voxel-set-type computational domains. These domains typically stem from mu CT (micro computed tomography) imaging of porous rock and approximate a (on mu m scale) smooth domain with a certain resolution Planar surfaces that are perpendicular to the main axes are naturally approximated by a layer of voxels However, planar surfaces in any other directions and curved surfaces yield a jagged/topologically rough surface approximation by voxels. For the standard Cahn-Hilliard formulation, where the contact angle between the diffuse interface and the domain boundary (fluid-solid interface/wall) is 90 degrees, jagged surfaces have no impact on the contact angle. However, a prescribed contact angle smaller or larger than 90 degrees on jagged voxel surfaces is amplified. As a remedy, we propose the introduction of surface energy correction factors for each fluid-solid voxel face that counterbalance the difference of the voxel-set surface area with the underlying smooth one. The discretization of the model equations is performed with the discontinuous Galerkin method However, the presented semi-analytical approach of correcting the surface energy is equally applicable to other direct numerical methods such as finite elements, finite volumes, or finite differences, since the correction factors appear in the strong formulation of the model. (C) 2018 Elsevier Inc. All rights reserved.}, author = {Frank, Florian and Liu, Chen and Scanziani, Alessio and Alpak, Faruk Omer and Rivière, Béatrice}, doi = {10.1016/j.jcis.2018.02.075}, faupublication = {yes}, journal = {Journal of Colloid and Interface Science}, keywords = {Cahn-Hilliard equation;Contact angle;Jagged surface;Topologically rough surface;mu CT imaging;Porous media}, pages = {282–291}, peerreviewed = {Yes}, title = {{An} energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods}, volume = {523}, year = {2018} } @incollection{faucris.122059124, author = {Marheineke, Nicole}, booktitle = {Progress in Industrial Mathematics at ECMI 2002}, editor = {A. D. Fitt, A. Buikis, R. Ciegis}, faupublication = {no}, pages = {81-90}, peerreviewed = {unknown}, publisher = {Springer}, title = {{Modified} {FEM} for fibre-fluid interactions}, year = {2004} } @article{faucris.121684684, author = {Grün, Günther and Rumpf, Martin}, faupublication = {no}, journal = {Numerische Mathematik}, pages = {113-152}, peerreviewed = {Yes}, title = {{Nonnegativity} preserving convergent schemes for the thin film equation}, volume = {87}, year = {2000} } @article{faucris.116669564, author = {Grün, Günther and Rumpf, Martin}, faupublication = {no}, journal = {European Journal of Applied Mathematics}, pages = {293-320}, peerreviewed = {Yes}, title = {{Simulation} of singularities and instabilities in thin film flow}, volume = {12}, year = {2001} } @article{faucris.204144050, author = {Rupp, Andreas and Knabner, Peter}, doi = {10.1002/num.22150}, faupublication = {yes}, journal = {Numerical Methods For Partial Differential Equations}, keywords = {instationary Darcy problem; error analysis; stability analysis; local discontinuous Galerkin method}, pages = {1374-1394}, peerreviewed = {Yes}, title = {{Convergence} order estimates of the local discontinuous {Galerkin} method for instationary {Darcy} flow}, volume = {33}, year = {2017} } @article{faucris.106893864, abstract = {In this paper we analyze a fully practical piecewise linear finite element approximation involving numerical integration, backward Euler time discretization, and possibly regularization of the following degenerate parabolic system arising in a model of reactive solute transport in porous media: find {u(x, t),v(x,t)} such that ∂u + ∂v- Δu = f in Ω × (0,T] u = 0 on ∂Ω × (0,T] ∂v = k((℘(u) - v) in Ω × (0, T] u(·,0) = g1(·) v(·,0) = g2(·) in Ω ⊂ R, 1≤d≤3 for given data k ∈ R, f, g1, g2 and a monotonically increasing ℘ ∈ C(R) ∩ C(-∞,0] ∪ (0,∞) satisfying ℘(0) = 0, which is only locally Hölder continuous with exponent p ∈ (0,1) at the origin, e.g., ℘(s) ≡ [s] . This lack of Lipschitz continuity at the origin limits the regularity of the unique solution {u,v} and leads to difficulties in the finite element error analysis.}, author = {Barrett, John W. and Knabner, Peter}, doi = {10.1137/S0036142993249024}, faupublication = {yes}, journal = {SIAM Journal on Numerical Analysis}, keywords = {Degenerate parabolic systems; Error analysis; Finite elements; Porous medium}, pages = {201-227}, peerreviewed = {Yes}, title = {{Finite} {Element} {Approximation} of the {Transport} of {Reactive} {Solutes} in {Porous} {Media}. {Part} 1: {Error} {Estimates} for {Nonequilibrium} {Adsorption} {Processes}}, url = {http://epubs.siam.org/doi/abs/10.1137/S0036142993249024}, volume = {34}, year = {1997} } @incollection{faucris.116677484, author = {Arne, Walter and Rivero-Rodriguez, Javier and Pérez-Saborid, Miguel and Marheineke, Nicole and Wegener, Raimund}, booktitle = {Progress in Industrial Mathematics at ECMI 2014}, faupublication = {yes}, peerreviewed = {unknown}, publisher = {Springer}, title = {{Homotopy} method for viscous {Cosserat} rod model describing electrospinning}, year = {2016} } @article{faucris.208178412, abstract = {Hierarchical scale separation (HSS) is an iterative two-scale approximation method for large sparse systems of linear equations arising from discontinuous Galerkin (DG) discretizations. HSS splits the linear system into a coarse-scale system of reduced size corresponding to the local mean values of the solution, and a set of decoupled local fine-scale systems corresponding to the higher order solution components. This scheme then alternates between coarse-scale and fine-scale system solves until both components converge. The motivation of HSS is to promote parallelism by decoupling the fine-scale systems, and to reduce the communication overhead from classical linear solvers by only applying them to the coarse-scale system.

We propose a modified HSS scheme (“inexact HSS”, “IHSS”) that exploits the highly parallel fine-scale solver more extensively and only approximates the coarse-scale solution in every iteration thus resulting in a significant speedup. The tolerance of the coarse-scale solver is adapted in every IHSS cycle, controlled by the residual norm of the fine-scale system. Anderson acceleration is employed in the repeated solving of the fine-scale system to stabilize the scheme. We investigate the applicability of IHSS to systems stemming from the nonsymmetric interior penalty DG discretization of the Cahn–Hilliard equation, discuss its hybrid parallel implementation for large-scale simulations, and compare the performance of a widely used iterative solver with and without IHS}, author = {Thiele, Christopher and Araya-Polo, Mauricio and Alpak, Faruk Omer and Rivière, Béatrice and Frank, Florian}, doi = {10.1016/j.camwa.2017.06.025}, faupublication = {no}, journal = {Computers & Mathematics With Applications}, keywords = {discontinuous Galerkin method; sparse linear solver; hierarchical scale separation; parallel computing; p-multigrid method; modal basis}, pages = {1769–1778}, peerreviewed = {Yes}, title = {{Inexact} hierarchical scale separation: a two-scale approach for linear systems from discontinuous {Galerkin} discretizations}, url = {https://www.sciencedirect.com/science/article/pii/S0898122117303735?via=ihub}, volume = {74}, year = {2017} } @article{faucris.116669124, author = {Grün, Günther}, faupublication = {no}, journal = {Zeitschrift für Analysis und ihre Anwendungen}, pages = {987-998}, peerreviewed = {Yes}, title = {{On} {Bernis}' interpolation inequalities in multiple space dimensions}, volume = {20}, year = {2001} } @article{faucris.117782324, abstract = {The application of natural attenuation as a site remediation strategy depends essentially on the reliable prediction of the migration of the contaminant plume. We present a one-dimensional simulation tool that is capable of handling a variety of complex scenarios predicted to be of interest in site remediation problems. The implementation of the different components is organized in a modular structure that facilitates arbitrary extensions of the incorporated models and enables the model components to be combined. Efficient, robust numerical techniques (e.g. hybrid mixed finite elements) are embedded in a menu driven, user-friendly environment to serve hydrogeologists or engineers without profound knowledge of the mathematical theory. The software is suitable for Unix workstations as well as inexpensive personal computers. The model components include reactive solute transport (with diffusion, dispersion, advection and sorption) and single- as well as two-phase flow in the saturated and the vadose zone. The underlying models contain non-standard effects that enable the simulation of a large variety of relevant support strategies for natural attenuation. We present examples for the interaction of the transport of surface-active agents and the water flow or the influence of carriers, which can change predicted residence and travel times of strongly sorbing contaminants by several orders of magnitude.}, author = {Schneid, Eckhard and Prechtel, Alexander and Knabner, Peter}, faupublication = {yes}, journal = {Land Contamination and Reclamation}, keywords = {Carrier facilitation; Finite elements; Numerical flow and transport model; Simulation software; Surfactants}, pages = {357-365}, peerreviewed = {unknown}, title = {{A} comprehensive tool for the simulation of complex reactive transport and flow in soils}, volume = {8}, year = {2000} } @article{faucris.121151844, author = {Grün, Günther}, faupublication = {no}, journal = {Zeitschrift für Analysis und ihre Anwendungen}, pages = {541-573}, peerreviewed = {Yes}, title = {{Degenerate} parabolic equations of fourth order and a plasticity model with nonlocal hardening}, volume = {14}, year = {1995} } @article{faucris.123423564, abstract = {In this article a method is proposed for the efficient simulation of reactive systems or reactive transport problems including (equilibrium) mineral precipitation-dissolution. The difficulty lies in the fact that for larger systems it is usually a priorily not known for which mineral the fluid is saturated and for which it is undersaturated. Currently wide-spread algorithms use some trial-and-error strategy requiring repeated computations, or an approximation of equilibrium precipitation-dissolution by a kinetic description. In this article we propose to formulate the problem as a so-called complementarity problem (CP) and to solve it with the semismooth Newton method, a solution strategy well known in the field of optimization theory. The CP formulation of the mineral reactions is then combined with a reformulation for the full multicomponent reactive transport problem which leads to a reduction of the number of unknowns. The reactive transport problem is tackled in the sense of a one step (global implicit) method. © 2010 Elsevier Ltd.}, author = {Kräutle, Serge}, doi = {10.1016/j.advwatres.2010.10.004}, faupublication = {yes}, journal = {Advances in Water Resources}, keywords = {Reactive transport; Minerals; Complementarity problems; Semismooth Newton method}, pages = {137-151}, peerreviewed = {Yes}, title = {{The} semismooth {Newton} method for multicomponent reactive transport with minerals}, url = {http://www.sciencedirect.com/science/article/pii/S0309170810001934}, volume = {34}, year = {2011} } @article{faucris.121236764, abstract = {This work deals with the modeling and simulation of slender viscous jets exposed to gravity and rotation, as they occur in rotational spinning processes. In terms of slender-body theory, we show the asymptotic reduction of a viscous Cosserat rod to a string system for vanishing slenderness parameter. We propose two string models, i.e. inertial and viscous-inertial string models, that differ in the closure conditions and hence yield a boundary value problem and an interface problem, respectively. We investigate the existence regimes of the string models in the four-parametric space of Froude, Rossby, Reynolds numbers and jet length. The convergence regimes where the respective string solution is the asymptotic limit to the rod turn out to be disjoint and to cover nearly the whole parameter space. We explore the transition hyperplane and derive analytically low and high Reynolds number limits. Numerical studies of the stationary jet behavior for different parameter ranges complete the work. © 2011 World Scientific Publishing Company.}, author = {Arne, Walter and Marheineke, Nicole and Wegener, Raimund}, doi = {10.1142/S0218202511005635}, faupublication = {yes}, journal = {Mathematical Models & Methods in Applied Sciences}, keywords = {asymptotic limits; boundary value problems; inertial and viscous-inertial fiber regimes; Rotational spinning processes; slender-body theory}, pages = {1987-2018}, peerreviewed = {Yes}, title = {{Asymptotic} transition from cosserat rod to string models for curved viscous inertial jets}, volume = {21}, year = {2011} } @article{faucris.110044484, author = {Totsche, Kai Uwe and Amelung, Wulf and Gerzabek, M. H. and Guggenberger, Georg and Klumpp, Erwin and Knief, Claudia and Lehndorff, Eva and Mikutta, Robert and Peth, Stephan and Prechtel, Alexander and Ray, Nadja and Kögel-Knabner, Ingrid}, doi = {10.1002/jpln.201600451}, faupublication = {yes}, journal = {Journal of Plant Nutrition and Soil Science}, pages = {104-136}, peerreviewed = {Yes}, title = {{Microaggregates} in {Soils}}, url = {http://onlinelibrary.wiley.com/doi/10.1002/jpln.201600451/full}, volume = {181}, year = {2018} } @masterthesis{faucris.209591150, author = {Prechtel, Alexander}, faupublication = {no}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{La} pollution d'un site par des hydrocarbures - aspects de la modélisation hydrogéologique et étude géostatistique}, year = {1998} } @article{faucris.215694480, abstract = {In this paper, we are concerned with the numerical treatment of a recent diffuse interface model for two-phase flow of electrolyte solutions (Campillo-Funollet et al., SIAM J. Appl. Math. 72(6), 1899-1925, 2012) . This model consists of a Nernst-Planck-system describing the evolution of the ion densities and the electrostatic potential which is coupled to a Cahn-Hilliard-Navier-Stokes-system describing the evolution of phase-field, velocity field, and pressure. In the first part, we present a stable, fully discrete splitting scheme, which allows to split the governing equations into different blocks, which may be treated sequentially and thereby reduces the computational costs significantly. This scheme comprises different mechanisms to reduce the induced numerical dissipation. In the second part, we investigate the impact of these mechanisms on the scheme's sensitivity to the size of the time increment using the example of a falling droplet. Finally, we shall present simulations showing ion induced changes in the topology of charged droplets serving as a qualitative validation for our discretization and the underlying model.}, author = {Metzger, Stefan}, doi = {10.1007/s11075-018-0530-2}, faupublication = {yes}, journal = {Numerical Algorithms}, note = {CRIS-Team WoS Importer:2019-04-09}, pages = {1361-1390}, peerreviewed = {Yes}, title = {{On} stable, dissipation reducing splitting schemes for two-phase flow of electrolyte solutions}, volume = {80}, year = {2019} } @article{faucris.117797064, abstract = {We present here the definition of the reactive transport benchmark of Groupement Mathematical Modeling and Numerical Simulation for Nuclear Waste Management Problems. The aim of this benchmark is to propose a challenging test for numerical methods used for reactive transport modeling in porous media. In order to focus on numerical methods, the problem presented here is of quite a small size, both from a hydrodynamical and from a geochemical point of view. Though the chemical coefficients used in this benchmark are not taken from a real chemical system, they are realistic, and the test case is quite challenging. © Springer Science + Business Media B.V. 2009.}, author = {Carrayrou, Jérôme and Kern, Michel and Knabner, Peter}, doi = {10.1007/s10596-009-9157-7}, faupublication = {yes}, journal = {Computational Geosciences}, keywords = {Benchmark; MoMaS; Porous media; Reactive transport}, pages = {385-392}, peerreviewed = {Yes}, title = {{Reactive} transport benchmark of {MoMaS}}, volume = {14}, year = {2010} } @article{faucris.123855864, abstract = {Accurate identification of interactions of reactive solutes with porous media constituents is necessary for reliable risk assessment studies and the development of efficient sanitation strategies. Standard parameter estimation procedures bear a number of unsolved problems with respect to uniqueness and identifiability. This paper presents a new approach for the identification of nonlinear interaction parameters of column outflow experiments. The procedure requires no a priori assumptions on the shape of the underlying interaction process functions. Employing experimental data sets on cadmium and anthracene breakthrough as case studies, possible applications of the new approach will be shown, and its features will be discussed. Error analysis based on singular value decomposition of the sensitivity matrix quantifies the identification error. Identification procedures without a priori shape information are superior to fixed parametrizations in diagnostic investigations, especially in cases without reliable a priori knowledge on the sorptive interactions. © Springer 2006.}, author = {Knabner, Peter and Igler, B. A. and Totsche, Kai Uwe and DuChateau, Paul}, doi = {10.1007/s10596-005-9008-0}, faupublication = {yes}, journal = {Computational Geosciences}, keywords = {Adaptation; Breakthrough experiment; Identification; Inverse problems; Output least squares minimization; Sorption}, pages = {203-217}, peerreviewed = {Yes}, title = {{Unbiased} identification of nonlinear sorption characteristics by soil column breakthrough experiments}, volume = {9}, year = {2005} } @incollection{faucris.107387984, abstract = {Diffuse interface models have become an important analytical and numerical method to model two-phase flows. In this contribution we review the subject and discuss in detail a thermodynamically consistent model with a divergence free velocity field for two-phase flows with different densities. The model is derived using basic thermodynamical principles, its sharp interface limits are stated, existence results are given, different numerical approaches are discussed and computations showing features of the model are presented.}, author = {Grün, Günther and Metzger, Stefan and Abels, Helmut and Garcke, Harald}, booktitle = {Advances in Mathematical Fluid Mechanics}, faupublication = {yes}, pages = {203-229}, peerreviewed = {Yes}, publisher = {springer}, series = {Transport processes at fluidic interface}, title = {{Diffuse} interface models for incompressible two-phase flows with different densities}, year = {2017} } @article{faucris.117786944, abstract = {A two-scale model for liquid-solid phase transitions with equiaxed dendritic microstructure in binary material in the case of slow solute diffusion is presented. The model consists of a macroscopic energy transport equation and, for each point of the macroscopic domain, a local cell problem describing the evolution of the microstructure and the microsegregation. It is derived by formal homogenization of a sharp interface model, including the Gibbs-Thomson law and kinetic undercooling. Based on the two-scale model, a numerical two-scale method for the simulation of phase transitions with dendritic microstructure is developed, and numerical examples are presented. © 2002 Elsevier Science (USA}, author = {Eck, Christof and Knabner, Peter and Korotov, Sergey}, doi = {10.1006/jcph.2002.7018}, faupublication = {yes}, journal = {Journal of Computational Physics}, keywords = {Crystal growth; Gibbs-Thomson law; Homogenization; Kinetic undercooling; Multiscale model; Stefan problem}, pages = {58-80}, peerreviewed = {Yes}, title = {{A} two-scale method for the computation of solid-liquid phase transitions with dendritic microstructure}, volume = {178}, year = {2002} } @incollection{faucris.107386004, abstract = {

We derive a diffuse-interface model for two-phase flow of incompressible fluids with dissolved noninteracting polymers. Describing the polymers as bead chains governed by general elastic spring potentials, including in particular Hookean and finitely extensible, nonlinear elastic (FENE) potentials, it couples a Fokker-Planck type equation describing distribution and orientation of the polymer chains with Cahn–Hilliard and Navier–Stokes type equations describing the balance of mass and momentum. Allowing for different solubility properties which are modelled by Henry type energy functionals, the presented model covers the case of one Newtonian fluid and one non-Newtonian fluid as well as the case of two non-Newtonian fluids. In the case of Hookean spring potentials, we derive a macroscopic diffuse-interface model for two-phase flow of Oldroyd-B-type liquids.

In the case of dumbbell models, we show existence of solutions and present numerical simulations in two space dimensions on oscillating polymeric droplets.

}, author = {Grün, Günther and Metzger, Stefan}, booktitle = {Advances in Mathematical Fluid Mechanics}, faupublication = {yes}, pages = {291-303}, peerreviewed = {Yes}, publisher = {Springer}, series = {Transport processes at fluidic interfaces}, title = {{Micro}-macro-models for two-phase flow of dilute polymeric solutions: macroscopic limit, analysis, numerics}, year = {2017} } @article{faucris.205334100, author = {Burger, Martin and et al.}, author_hint = {Schuster T, Hahn B, Burger M}, doi = {10.1088/1361-6420/aab0f5}, faupublication = {no}, journal = {Inverse Problems}, peerreviewed = {Yes}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{Dynamic} inverse problems: modelling-regularization-numerics {Preface}}, volume = {34}, year = {2018} } @misc{faucris.122381424, author = {Kräutle, Serge}, faupublication = {yes}, peerreviewed = {automatic}, title = {{General} multi-species reactive transport problems in porous media: {Efficient} numerical approaches and existence of global solutions}, year = {2008} } @article{faucris.119193844, abstract = {This paper is a prequel to that of Marchand et al. (Comput Geosci 16:691-708, 2012), where an efficient and accurate hybrid-mixed finite element approximation for a system of time-dependent nonlinear conservation equations has been formulated, implemented, and tested, which are general enough to represent most of the existing formulations for two-component liquid-gas flow in porous medium with phase exchange, also allowing for any (dis)appearance of one of the phases. Temperature variation is neglected, but capillary effects are included by extended Darcy's law, and Fickian diffusion is taken into account. The efficiency and stability of the numerical method of Lake (1989) relies on an equivalent reformulation of the otherwise commonly used model in terms of new principal variables and subsequent static (flash) equations allowing more generally for any (dis)appearance of one of the phases without the need of variable switching or unphysical quantities. In particular, the formulation in terms of complementarity conditions allows for an efficient and stable solution by the semismooth Newton's method. © 2013 Springer Science+Business Media Dordrecht.}, author = {Marchand, Estelle and Müller, Torsten and Knabner, Peter}, doi = {10.1007/s10596-013-9341-7}, faupublication = {yes}, journal = {Computational Geosciences}, keywords = {Complementarity problems; Compositional multiphase flow; Nonlinear PDEs}, pages = {431-442}, peerreviewed = {Yes}, title = {{Fully} coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. {Part} {I}: {Formulation} and properties of the mathematical model}, volume = {17}, year = {2013} } @article{faucris.117793544, abstract = {We consider colloidal dynamics and single-phase fluid flow within a saturated porous medium in two space dimensions. A new approach in modeling pore clogging and porosity changes on the macroscopic scale is presented. Starting from the pore scale, transport of colloids is modeled by the Nernst-Planck equations. Here, interaction with the porous matrix due to (non-)DLVO forces is included as an additional transport mechanism. Fluid flow is described by incompressible Stokes equations with interaction energy as forcing term. Attachment and detachment processes are modeled by a surface reaction rate. The evolution of the underlying microstructure is captured by a level set function. The crucial point in completing this model is to set up appropriate boundary conditions on the evolving solid-liquid interface. Their derivation is based on mass conservation. As a result of an averaging procedure by periodic homogenization in a level set framework, on the macroscale we obtain Darcy's law and a modified averaged convection-diffusion equation with effective coefficients due to the evolving microstructure. These equations are supplemented by microscopic cell problems. Time- and space-dependent averaged coefficient functions explicitly contain information of the underlying geometry and also information of the interaction potential. The theoretical results are complemented by numerical computations of the averaged coefficients and simulations of a heterogeneous multiscale scenario. Here, we consider a radially symmetric setting, i. e., in particular we assume a locally periodic geometry consisting of circular grains. We focus on the interplay between attachment and detachment reaction, colloidal interaction forces, and the evolving microstructure. Our model contributes to the understanding of the effects and processes leading to porosity changes and pore clogging from a theoretical point of view. © 2012 Springer Science+Business Media B.V.}, author = {Ray, Nadja and van Noorden, Tycho and Frank, Florian and Knabner, Peter}, doi = {10.1007/s11242-012-0068-z}, faupublication = {yes}, journal = {Transport in Porous Media}, keywords = {Colloidal transport; Evolving microstructure; Level set function; Mixed finite elements; Multiscale coefficients; Particle-surface interaction; Periodic homogenization; Pore clogging; Pore scale modeling; Porosity changes}, pages = {669-696}, peerreviewed = {Yes}, title = {{Multiscale} {Modeling} of {Colloid} and {Fluid} {Dynamics} in {Porous} {Media} {Including} an {Evolving} {Microstructure}}, volume = {95}, year = {2012} } @article{faucris.119215844, abstract = {We perform the periodic homogenization (i.e ε → 0) of a non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where ε is a suitable scale parameter. The objective is to investigate the influence of different boundary conditions and variable choices of scalings in ε of the microscopic system of partial differential equations on the structure of the (upscaled) limit model equations. Due to the specific nonlinear coupling of the underlying equations, special attention has to be paid when passing to the limit in the electrostatic drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained. © 2012 Elsevier Inc.}, author = {Ray, Nadja and Muntean, Adrian and Knabner, Peter}, doi = {10.1016/j.jmaa.2012.01.052}, faupublication = {yes}, journal = {Journal of Mathematical Analysis and Applications}, keywords = {Colloidal transport; Homogenization; Porous media; Stokes-Nernst-Planck-Poisson system; Two-scale convergence}, pages = {374-393}, peerreviewed = {Yes}, title = {{Rigorous} homogenization of a {Stokes}-{Nernst}-{Planck}-{Poisson} system}, volume = {390}, year = {2012} } @article{faucris.211500005, abstract = {We construct a Galerkin finite element method for the numerical approximation of weak solutions to a recent micro-macro bead-spring model for two-phase flow of dilute polymeric solutions derived by methods from nonequilibrium thermodynamics ([Grun, Metzger, M3AS 26 (2016) 823-866]). The model consists of Cahn-Hilliard type equations describing the evolution of the fluids and the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three spatial dimensions for the velocity and the pressure of the fluids with an elastic extra-stress tensor on the right-hand side in the momentum equation which originates from the presence of dissolved polymer chains. The polymers are modeled by dumbbells subjected to a finitely extensible, nonlinear elastic (FENE) spring-force potential. Their density and orientation are described by a Fokker-Planck type parabolic equation with a center-of-mass diffusion term. We perform a rigorous passage to the limit as the spatial and temporal discretization parameters simultaneously tend to zero, and show that a subsequence of these finite element approximations converges towards a weak solution of the coupled Cahn-Hilliard-Navier-Stokes-Fokker-Planck system. To underline the practicality of the presented scheme, we provide simulations of oscillating dilute polymeric droplets and compare their oscillatory behaviour to the one of Newtonian droplets.}, author = {Metzger, Stefan}, doi = {10.1051/m2an/2018042}, faupublication = {yes}, journal = {Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique}, note = {CRIS-Team WoS Importer:2019-02-21}, pages = {2357-2408}, peerreviewed = {Yes}, title = {{ON} {CONVERGENT} {SCHEMES} {FOR} {TWO}-{PHASE} {FLOW} {OF} {DILUTE} {POLYMERIC} {SOLUTIONS}}, volume = {52}, year = {2019} } @incollection{faucris.116672204, author = {Grün, Günther and Rumpf, Martin}, booktitle = {Finite volume schemes for complex applications II}, editor = {R. Vilsmeier, F. Benkhaldoun, D. Hänel}, faupublication = {no}, peerreviewed = {unknown}, publisher = {Hermes Science Publications, Paris}, title = {{Entropy} consistent finite volume schemes for the thin film equation}, year = {1999} } @article{faucris.122287044, abstract = {In this paper we present a chain of mathematical models that enables the numerical simulation of the airlay process and the investigation of the resulting nonwoven material by means of virtual tensile strength tests. The models range from a highly turbulent dilute fiber suspension flow to stochastic surrogates for fiber lay-down and web formation and further to Cosserat networks with effective material laws. Crucial is the consistent mathematical mapping between the parameters of the process and the material. We illustrate the applicability of the model chain for an industrial scenario, regarding data from computer tomography and experiments. By this proof of concept we show the feasibility of future simulation-based process design and material optimization which are long-term objectives in the technical textile industry.}, author = {Gramsch, Simone and Klar, Axel and Leugering, Günter and Marheineke, Nicole and Nessler, Christian and Strohmeyer, Christoph and Wegener, Raimund}, doi = {10.1186/s13362-016-0034-4}, faupublication = {yes}, journal = {Journal of Mathematics in Industry}, keywords = {airlay process; effective material laws; fiber lay-down; fiber networks; fiber suspension flow; homogenization; model chain; nonwoven material; stochastic surrogates; virtual tensile strength test}, peerreviewed = {unknown}, title = {{Aerodynamic} web forming: process simulation and material properties}, volume = {6}, year = {2016} } @article{faucris.106897164, abstract = {We consider mixed finite element discretization for a class of degenerate parabolic problems including the Richards' equation. After regularization, time discretization is achieved by an Euler implicit scheme, while mixed finite elements are employed for the discretization in space. Based on the results obtained in (Radu et al. RANA Preprint 02-06, Eindhoven University of Technology, 2002), this paper considers a simple iterative scheme to solve the emerging nonlinear elliptic problems. © 2003 Elsevier B.V. All rights reserved.}, author = {Pop, Iuliu Sorin and Radu, Adrian Florin and Knabner, Peter}, doi = {10.1016/j.cam.2003.04.008}, faupublication = {yes}, journal = {Journal of Computational and Applied Mathematics}, keywords = {Degenerate parabolic problems; Euler implicit scheme; Linearization; Mixed finite elements; Regularization; Richards' equation}, pages = {365-373}, peerreviewed = {Yes}, title = {{Mixed} finite elements for the {Richards}' equation: {Linearization} procedure}, volume = {168}, year = {2004} } @article{faucris.119193184, abstract = {We consider the modeling and simulation of compositional two-phase flow in a porous medium, where one phase is allowed to vanish or appear. The modeling of Marchand et al. (in review) leads to a nonlinear system of two conservation equations. Each conservation equation contains several nonlinear diffusion terms, which in general cannot be written as a function of the gradients of the two principal unknowns. Also the diffusion coefficients are not necessarily explicit local functions of them. For the generalised mixed finite elements approximation, Lagrange multipliers associated to each principal unknown are introduced, the sum of the diffusive fluxes of each component is explicitly eliminated and the static condensation leads to a "global" nonlinear system of equations only in the Lagrange multipliers also including complementarity conditions to cope with vanishing or appearing phases. After time discretisation, this system can be solved at each time step using a semi-smooth Newton method. The static condensation involves "local" nonlinear systems of equations associated to each element, solved also by a semismooth Newton method. The algorithm is successfully applied to 1D and 2D examples of water-hydrogen flow involving gas phase appearance and disappearance. © 2012 Springer Science+Business Media B.V.}, author = {Marchand, Estelle and Müller, Torsten and Knabner, Peter}, doi = {10.1007/s10596-012-9279-1}, faupublication = {yes}, journal = {Computational Geosciences}, keywords = {Mixed hybrid finite elements; Nonlinear systems of partial differential equations}, pages = {691-708}, peerreviewed = {Yes}, title = {{Fully} coupled generalised hybrid-mixed finite element approximation of two-phase two-component flow in porous media. {Part} {II}: {Numerical} scheme and numerical results}, volume = {16}, year = {2012} } @article{faucris.122614404, abstract = {A parameter identification problem for the hydraulic properties of porous media is considered. Numerically, this inverse problem is solved by minimizing an output least-squares functional. The unknown hydraulic properties which are nonlinear coefficients of a partial differential equation are approximated by spline functions. The identification is embedded into a multi-level algorithm and coupled with a linear sensitivity analysis to describe the ill-posedness of the inverse problem. © 2002 Elsevier Science B.V. All rights reserved.}, author = {Bitterlich, Sandro and Knabner, Peter}, doi = {10.1016/S0377-0427(02)00430-2}, faupublication = {yes}, journal = {Journal of Computational and Applied Mathematics}, keywords = {Adjoint method; Direct method; Inverse problem; Multi-level algorithm; Parameter identification; Sensitivity analysis}, pages = {153-173}, peerreviewed = {Yes}, title = {{An} efficient method for solving an inverse problem for the {Richards} equation}, volume = {147}, year = {2002} } @article{faucris.106902664, abstract = {Biodegradable collagen matrices have become a promising alternative to synthetic polymers as drug delivery systems for sustained release. Previously, a mathematical model describing water penetration, matrix swelling and drug release by diffusion from dense collagen matrices was introduced and tested (cf. Radu et al. in J. Pharm. Sci. 91:964-972, 2002). However, enzymatic matrix degradation influences the drug release as well. Based on experimental studies (cf. Metzmacher in Enzymatic degradation and drug release behavior of dense collagen implants. Ph.D. thesis, LMU University of Munich, 2005), a mathematical model is presented here that describes drug release by collagenolytic matrix degradation. Existence and uniqueness of a solution of the model equations is reviewed. A mixed Raviart-Thomas finite element discretization for solving the coupled system of partial and ordinary differential equations is proposed and analyzed theoretically. The model is verified by a comparison of numerically calculated and experimentally measured data and, in particular, investigated by a parameter sensitivity study. For illustration, some concentration profiles of a twodimensional simulation are shown. © The Author(s) 2008.}, author = {Radu, F. A. and Bause, Markus and Knabner, Peter and Friess, W. and Metzmacher, I.}, doi = {10.1007/s00791-008-0118-9}, faupublication = {yes}, journal = {Computing and Visualization in Science}, pages = {409-420}, peerreviewed = {unknown}, title = {{Numerical} simulation of drug release from collagen matrices by {Enzymatic} degradation}, volume = {12}, year = {2009} } @article{faucris.205335966, abstract = {We consider the inverse problem of recovering an unknown functional parameter u in a separable Banach space, from a noisy observation vector y of its image through a known possibly non-linear map G. We adopt a Bayesian approach to the problem and consider Besov space priors (see Lassas et al (2009 Inverse Problems Imaging 3 87-122)), which are well-known for their edge-preserving and sparsity-promoting properties and have recently attracted wide attention especially in the medical imaging community.Our key result is to show that in this non-parametric setup the maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. This is done independently for the so-called weak and strong MAP estimates, which as we show coincide in our context. In addition, we prove a form of weak consistency for the MAP estimators in the infinitely informative data limit. Our results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on non-parametric MAP estimates. Second, the result analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.}, author = {Burger, Martin and et al.}, author_hint = {Agapiou S, Burger M, Dashti M, Helin T}, doi = {10.1088/1361-6420/aaacac}, faupublication = {no}, journal = {Inverse Problems}, keywords = {Bayesian inverse problems;Besov prior;MAP estimators}, peerreviewed = {Yes}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{Sparsity}-promoting and edge-preserving maximum a posteriori estimators in non-parametric {Bayesian} inverse problems}, url = {https://arxiv.org/pdf/1705.03286.pdf}, volume = {34}, year = {2018} } @article{faucris.122842544, abstract = {We present a method to transform the governing equations of multispecies reactive transport in porous media. The reformulation leads to a smaller problem size by decoupling of equations and by elimination of unknowns, which increases the efficiency of numerical simulations. The reformulation presented here is a generalization of earlier works. In fact, a whole class of transformations is now presented. This class is parametrized by the choice of certain transformation matrices. For specific choices, some known formulations of reactive transport can be retrieved. Hence, the software based on the presented transformation can be used to obtain efficiency comparisons of different solution approaches. For our efficiency tests, we use the MoMaS benchmark problem on reactive transport. © 2012 Springer Science+Business Media B.V.}, author = {Hoffmann, Joachim and Kräutle, Serge and Knabner, Peter}, doi = {10.1007/s10596-012-9304-4}, faupublication = {yes}, journal = {Computational Geosciences}, keywords = {Global implicit approach; Numerical simulation; Porous media; Reactive transport; Reduction of problem size}, pages = {1081-1099}, peerreviewed = {Yes}, title = {{A} general reduction scheme for reactive transport in porous media}, volume = {16}, year = {2012} } @article{faucris.108420664, author = {Geveler, Markus and Reuter, Balthasar and Aizinger, Vadym and Göddeke, Dominik and Turek, Stefan}, doi = {10.1007/s00450-016-0324-5}, faupublication = {yes}, journal = {Computer Science - Research and Development}, pages = {225-234}, peerreviewed = {Yes}, title = {{Energy} efficiency of the simulation of three-dimensional coastal ocean circulation on modern commodity and mobile processors}, volume = {31}, year = {2016} } @article{faucris.118023664, abstract = {The conjugate gradient boundary iteration (CGBI) is a domain decomposition method for symmetric elliptic problems on domains with large aspect ratio. High efficiency is reached by the construction of preconditioners that are acting only on the subdomain interfaces. The theoretical derivation of the method and some numerical results revealing a convergence rate of 0.04-0.1 per iteration step are given in this article. For the solution of the local subdomain problems, both finite element (FE) and spectral Chebyshev methods are considered. © 2004 American Mathematical Society.}, author = {Kräutle, Serge}, doi = {10.1090/S0025-5718-04-01706-5}, faupublication = {yes}, journal = {Mathematics of Computation}, keywords = {Domain decomposition; FETI; Parallelization; Preconditioning}, pages = {1231-1256}, peerreviewed = {Yes}, title = {{A} domain decomposition method using efficient interface-acting preconditioners}, volume = {74}, year = {2005} } @article{faucris.119229924, abstract = {Optimal design problems for semiconductor devices with relevant thermal effects can be formulated by help of the energy transport model. In this paper we perform a sensitivity analysis to derive the first-order necessary condition for the optimization. Exploiting the special structure of the KKT system we use a special variant of the classical Gummel iteration to provide a very fast optimization algorithm. Numerical results for a ballistic diode underline the feasibility of our approach. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.}, author = {Drago, C.R. and Marheineke, Nicole and Pinnau, René}, doi = {10.1002/zamm.201100171}, faupublication = {yes}, journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik}, keywords = {Energy transport model; Fast optimal design; Gaussian doping profiles.; Semiconductor design}, pages = {700-705}, peerreviewed = {Yes}, title = {{Semiconductor} device optimization in the presence of thermal effects}, volume = {93}, year = {2013} } @article{faucris.107777604, abstract = {This is the first in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source MATLAB/GNU Octave toolbox. The intention of this ongoing project is to provide a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix/vector operations and is carefully documented; in addition, a direct mapping between discretization terms and code routines is maintained throughout. The present work focuses on a two-dimensional time-dependent diffusion equation with space/time-varying coefficients. The spatial discretization is based on the local discontinuous Galerkin formulation. Approximations of orders zero through four based on orthogonal polynomials have been implemented; more spaces of arbitrary type and order can be easily accommodated by the code structure.}, author = {Frank, Florian and Reuter, Balthasar and Aizinger, Vadym and Knabner, Peter}, doi = {10.1016/j.camwa.2015.04.013}, faupublication = {yes}, journal = {Computers and Mathematics with Applications}, keywords = {MATLAB; GNU Octave; Local discontinuous Galerkin method; Vectorization; Open source}, pages = {11 - 46}, peerreviewed = {Yes}, title = {{FESTUNG}: {A} {MATLAB}/{GNU} {Octave} toolbox for the discontinuous {Galerkin} method. {Part} {I}: {Diffusion} operator}, url = {http://www.sciencedirect.com/science/article/pii/S0898122115001820}, volume = {70}, year = {2015} } @incollection{faucris.123194984, author = {Lu, Y. and Marheineke, Nicole and Mohring, Jan}, booktitle = {PMS&A - Modelling, Simulation and Application}, faupublication = {yes}, peerreviewed = {unknown}, publisher = {Springer}, title = {{Interpolation} strategy for {BT}-based parametric {MOR} of gas pipeline-networks}, year = {2016} } @article{faucris.117788264, abstract = {We consider a numerical scheme for a class of degenerate parabolic equations, including both slow and fast diffusion cases. A particular example in this sense is the Richards equation modeling the flow in porous media. The numerical scheme is based on the mixed finite element method (MFEM) in space, and is of one step implicit in time. The lowest order Raviart-Thomas elements are used. Here we extend the results in Radu et al. (SIAM J Numer Anal 42:1452-1478, 2004), Schneid et al. (Numer Math 98:353-370, 2004) to a more general framework, by allowing for both types of degeneracies. We derive error estimates in terms of the discretization parameters and show the convergence of the scheme. The features of the MFEM, especially of the lowest order Raviart-Thomas elements, are now fully exploited in the proof of the convergence. The paper is concluded by numerical examples. © 2008 Springer-Verlag.}, author = {Radu, Adrian Florin and Pop, Iuliu Sorin and Knabner, Peter}, doi = {10.1007/s00211-008-0139-9}, faupublication = {yes}, journal = {Numerische Mathematik}, pages = {285-311}, peerreviewed = {Yes}, title = {{Error} estimates for a mixed finite element discretization of some degenerate parabolic equations}, volume = {109}, year = {2008} } @inproceedings{faucris.119486004, abstract = {We present a model to describe the simultaneous reactive transport in porous media of an arbitrary number of mobile and immobile species. The model includes the effects of advection, dispersion, sorption and degradation catalysed by microbial populations. The locally mass-conservative mixed hybrid finite element method (MHFEM) to discretize this system of coupled convection-diffusion-reaction equations and the algorithmic solution of the resulting nonlinear algebraic equations are described in detail. Further, new ideas regarding the discretization of the convective term are discussed. Finally a comparative numerical study (MHFEM versus conforming FEM) is presented.}, address = {Berlin, Heidelberg}, author = {Radu, Adrian Florin and Bause, Markus and Prechtel, Alexander and Attinger, Sabine}, booktitle = {Numerical Mathematics and Advanced Applications}, editor = {Kunisch K., Of G., Steinbach O.}, faupublication = {yes}, month = {Jan}, pages = {513-520}, peerreviewed = {unknown}, publisher = {Springer}, title = {{A} {Mixed} {Hybrid} {Finite} {Element} {Discretization} {Scheme} for {Reactive} {Transport} in {Porous} {Media}}, year = {2008} } @article{faucris.207687060, abstract = {Modeling the droplet nucleation process requires a molecular-scale approach to describe the interfacial tension (IFT) of spherical interfaces. Density gradient theory (DGT), also referred to as square gradient theory in some publications has been widely used to compute the IFT of many pure and mixed systems at the molecular scale. However, the application of DGT to droplet interfaces is limited by its setup in open systems, in which a stable droplet cannot be achieved. In this article, we propose a mass-conserved DGT model in a closed system, i.e. with no-flux boundary conditions, where no mass exchange is allowed with the outside environment. As opposed to the traditional approach, this model enforces a canonical ensemble and guarantees energy dissipation. The proposed model has been successfully applied to systems with planar as well as spherical interfaces, especially for droplet's IFT calculation in the nucleation process. By extending the DGT model from open to closed systems, we demonstrate the potential of DGT as an inhomogeneous model for a wider range of academic and industrial applications.pCO2, dissolved inorganic carbon (DIC), and

and dissolution and precipitation of immobile species present inside a porous medium. The

transport of mobile species in the pores is modeled by a system of semilinear parabolic

partial differential equations. The reactions amongst the mobile species are assumed to

be reversible, i.e. both forward and backward reactions are considered. These reversible

reactions lead to highly nonlinear reaction rate terms on the right-hand side of the partial

differential equations. This system of equations for the mobile species is complemented

by flux boundary conditions at the outer boundary. Furthermore, the dissolution and

precipitation of immobile species on the surface of the solid parts are modeled by mass

action kinetics which lead to a nonlinear precipitation term and a multivalued dissolution

term. The model is posed at the pore (micro) scale. The contribution of this paper is two-

fold: first we show the existence of a unique positive global weak solution for the coupled

systems and then we upscale (homogenize) the model from the micro scale to the macro

scale. For the existence of solution, some regularization techniques, Schaefer’s fixed point

theorem and Lyapunov type arguments have been used whereas the concepts of two-scale

convergence and periodic unfolding are used for the homogenization.

p) the travelling wave may exist. For

We have implemented a particular variant of the phase-field method (PFM) into the computational core of a pore-scale multiphase flow simulator, namely PMFS-PFM, for the numerical simulations of incompressible flows of two immiscible fluid phases. The implementation was discussed in a previous paper for rectangular prism-shaped fully-connected domains, e.g., for simulating two-phase flow in a 2D slit or a 3D duct (Alpak et al., 2016). In this paper, we discuss the recent developments on PMFS-PFM. The main components of the new work are (I) implementation of support for inactive cells in PMFS-PFM by extending the original finite-volume method-based discretizations of the underlying partial differential equations (PDEs) in order to solve realistic 3D pore-scale flow problems on rock volumes stemming from imaging, and (II) enhancing the performance of the simulator through implementation of modern sparse linear solvers and distributed parallel computing. It has been shown that the simulations performed on complex pore-scale domains are consistent with the physics of the immiscible two-phase displacement. The parallel scalability of the code is reasonably well varying between 50% and 86% on the investigated test cases of varying complexity. Results indicate that the more disconnected the pore-scale domains, the lower the parallel efficiency. It has been noted that there is a possibility of improving the parallel efficiency by exploring various grid subdivisions.

A Helmholtz free-energy-driven, thermodynamically-based diffuse-interface/phase-field method is used for the effective simulation of a large number of advecting interfaces, while honoring the interfacial tension. The advective Cahn–Hilliard (mass balance, energy dissipation) and Navier–Stokes (momentum balance, incompressibility) equations are coupled to each other within the phase-field framework. Wettability on rock-fluid interfaces is accounted for via an energy-penalty-based wetting (contact-angle) boundary condition. Individual balance equations are discretized by use of a flexible discontinuous Galerkin (DG) method. The discretization of the mass balance equation is semi-implicit in time using a convex–concave splitting of the energy term. The momentum balance equation is split from the incompressibility constraint by a projection method and linearized with a Picard splitting. Mass and momentum balance equations are coupled to each other via operator splitting and solved sequentially.

We discuss the mathematical model and its DG discretization and briefly introduce nonlinear and linear solution strategies. Numerical validation tests show optimal convergence rates for the DG discretization indicating the correctness of the numerical scheme and of its implementation. Physical validation tests demonstrate the consistency of the phase distribution and velocity fields simulated within our framework. Finally, two-phase flow simulations on two real pore-scale images demonstrate the utility of the pore-scale simulator. The direct pore-scale numerical simulation methodology rigorously takes into account the flow physics by directly acting on pore-scale images of rocks without remeshing. The proposed method is accurate, numerically robust, and exhibits the potential for tackling realistic problem},
author = {Frank, Florian and Liu, Chen and Alpak, Faruk Omer and Berg, Steffen and Rivière, Béatrice},
doi = {10.2118/182607-PA},
faupublication = {no},
journal = {Spe Journal},
keywords = {phase-field method; diffuse interface; digital rock; oil and gas; Cahn–Hilliard; contact angle},
pages = {1–18},
peerreviewed = {Yes},
title = {{Direct} numerical simulation of flow on pore-scale images using the phase-field method},
url = {https://www.onepetro.org/journal-paper/SPE-182607-PA},
volume = {23},
year = {2018}
}
@incollection{faucris.119497004,
author = {Cibis, Thomas and Marheineke, Nicole and Wegener, Raimund},
booktitle = {Progress in Industrial Mathematics at ECMI 2012},
faupublication = {yes},
pages = {109-117},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Asymptotic} modeling framework for fiber-flow interactions in a two-way coupling},
year = {2014}
}
@article{faucris.118023884,
abstract = {We prove the existence and uniqueness of time-global solutions for multi-species multi-reaction advection-diffusion-dispersion problems with mass action kinetics in the space W-p(2,1)([0, T] x Omega). The reaction terms of mass action kinetics may contain polynomial expressions of arbitrarily high order. The difficulty to obtain an a priori estimate for the semilinar system of PDEs is tackled with a special Lyapunov function.},
author = {Kräutle, Serge},
doi = {10.11948/2011034},
faupublication = {yes},
journal = {JOURNAL OF APPLIED ANALYSIS AND COMPUTATION},
keywords = {Existence of solutions;A priori estimate;Parabolic equations;Reactive transport;Mass action kinetics},
month = {Jan},
pages = {497-515},
peerreviewed = {unknown},
title = {{Existence} of global solutions of multicomponent reactive transport problems with mass action kinetics in porous media},
volume = {1},
year = {2011}
}
@article{faucris.121079024,
author = {Reuter, Balthasar and Aizinger, Vadym and Wieland, Manuel and Frank, Florian and Knabner, Peter},
doi = {10.1016/j.camwa.2016.08.006},
faupublication = {yes},
journal = {Computers and Mathematics with Applications},
pages = {1896-1925},
peerreviewed = {Yes},
title = {{FESTUNG}: {A} {MATLAB} /{GNU} {Octave} toolbox for the discontinuous {Galerkin} method. {Part} {II}: {Advection} operator and slope limiting},
url = {http://www.sciencedirect.com/science/article/pii/S0898122116304606},
volume = {72},
year = {2016}
}
@incollection{faucris.120500644,
abstract = {In many liquid-solid phase transitions, a specific dendritic microstructure of the phase interface is observed. In this contribution we present two-scale models capable to describe the evolution of equiaxed microstructure. The models are based either on a sharp interface model or on a phase field model for phase transitions in binary alloys. In both cases, a formal asymptotic expansion in terms of a scale parameter ε for the microstructure is carried out, with solute diffusivity scaling proportional to ε^{2}. In the limit ε→0 we obtain a two scale-model consisting of a macroscopic heat transport equation and, at each point of the macroscopic domain, of a local cell problem modeling the microsegregation and the evolution of the microstructure.},
address = {Berlin, Heidelberg},
author = {Eck, Christof and Knabner, Peter},
booktitle = {Multiscale Problems in Science and Technology},
doi = {10.1007/978-3-642-56200-6_7},
editor = {Nenad Antonić, C. J. van Duijn, Willi Jäger, Andro Mikelić},
faupublication = {yes},
isbn = {978-3-540-43584-6},
pages = {175-187},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Two}-{Scale} {Models} for {Liquid}-{Solid} {Phase} {Transitions} in {Binary} {Material} with {Equiaxed} {Microstructure}},
year = {2002}
}
@book{faucris.217114270,
abstract = {Dieses umfangreiche Vorlesungsskript war (zum Teil) Grundlage für meine Vorlesungen "Mathematik für die Informationswirtschaft" am KIT Karlsruhe und ist Grundlage für meine Vorlesungen "Mathematik für Ingenieure" an der FAU Erlangen-Nürnberg.

Das Buch basiert auf jahrzehntelanger Lehrerfahrung an der Universität Erlangen und wichtige Teile des Buches entstammen aus dort entstandenen Skripten.}, address = {Berlin-Heidelberg}, author = {Merz, Wilhelm and Knabner, Peter}, doi = {10.1007/978-3-642-29980-3}, edition = {1}, faupublication = {yes}, isbn = {978-3-642-29979-7}, peerreviewed = {unknown}, publisher = {Springer}, series = {Springer-Lehrbuch}, title = {{Mathematik} für {Ingenieure} und {Naturwissenschaftler}}, url = {http://www.springer.com/de/book/9783642299797}, year = {2013} } @article{faucris.117787164, abstract = {We present adaptive mixed hybrid finite element discretizations of the Richards equation, a nonlinear parabolic partial differential equation modeling the flow of water into a variably saturated porous medium. The approach simultaneously constructs approximations of the flux and the pressure head in Raviart-Thomas spaces. The resulting nonlinear systems of equations are solved by a Newton method. For the linear problems of the Newton iteration a multigrid algorithm is used. We consider two different kinds of error indicators for space adaptive grid refinement: superconvergence and residual based indicators. They can be calculated easily by means of the available finite element approximations. This seems attractive for computations since no additional (sub-)problems have to be solved. Computational experiments conducted for realistic water table recharge problems illustrate the effectiveness and robustness of the approach. © 2004 Elsevier Ltd. All rights reserved.}, author = {Bause, Markus and Knabner, Peter}, doi = {10.1016/j.advwatres.2004.03.005}, faupublication = {yes}, journal = {Advances in Water Resources}, keywords = {A posteriori error indicator; Mixed finite element method; Nonlinear elliptic-parabolic problem; Raviart-Thomas spaces; Saturated-unsaturated flow}, pages = {565-581}, peerreviewed = {Yes}, title = {{Computation} of variably saturated subsurface flow by adaptive mixed hybrid finite element methods}, volume = {27}, year = {2004} } @article{faucris.108994644, author = {Grün, Günther and Fontelos, Marco Antonio and Kindelan, U. and Klingbeil, Fabian}, faupublication = {yes}, journal = {Journal of Adhesion Science and Technology}, pages = {1805-1824}, peerreviewed = {Yes}, title = {{Numerical} simulation of static and dynamic electrowetting}, volume = {26}, year = {2012} } @article{faucris.116633484, abstract = {In [N. Marheineke and R. Wegener, SIAM J. Appl. Math., 66 (2006), pp. 1703-1726], an aerodynamic force concept for a general air drag model based on a stochastic k-ε description for a turbulent flow field is derived. The turbulence effects on the dynamics of a long, slender, elastic fiber are specifically modeled by a correlated random Gaussian force and in its asymptotic limit on a macroscopic fiber scale by Gaussian white noise with flow-dependent amplitude. The present paper states quantitative similarity estimates and numerical comparisons for the choice of a Taylor drag model in a given application. © 2007 Society for Industrial and Applied Mathematics.}, author = {Marheineke, Nicole and Wegener, Raimund}, doi = {10.1137/06065489X}, faupublication = {no}, journal = {SIAM Journal on Applied Mathematics}, keywords = {Air drag; ARMA process; Fiber-turbulence interaction scales; Flexible fibers; K-ε turbulence model; Random gaussian aerodynamic force; Stochastic differential equations; White noise}, pages = {1-23}, peerreviewed = {Yes}, title = {{Fiber} dynamics in turbulent flows: {Specific} taylor drag}, volume = {68}, year = {2007} } @article{faucris.109046124, author = {Grün, Günther and Bertozzi, Andrea L. and Witelski, Thomas}, faupublication = {no}, journal = {Nonlinearity}, pages = {1569-1592}, peerreviewed = {Yes}, title = {{Dewetting} films: {Bifurcations} and concentrations}, volume = {14}, year = {2001} } @article{faucris.117787824, abstract = {Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations for the one-point one-time PDF are usually based on systems of computational particles describee by Ito equations. We establish consistency conditions relating the concentration statistics to that of the Ito process and the solution of its associated Fokker-Planck equation to that of the PDF equation. In this frame, we use a recently proposed numerical method which approximates PDFs by particle densities obtained with a global random walk (GRW) algorithm. The GRW-PDF approach is illustrated for a problem of contaminant transport in groundwater.}, author = {Suciu, Nicolae and Schüler, Lennart and Radu, Adrian Florin and Attinger, Sabine and Vamo̧s, Cǎlin and Knabner, Peter}, doi = {10.1515/auom-2015-0055}, faupublication = {yes}, journal = {Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica}, keywords = {Mixing; PDF methods; Porous media; Random walk}, pages = {187-208}, peerreviewed = {unknown}, title = {{Consistency} issues in pdf methods}, volume = {23}, year = {2015} } @article{faucris.122161424, author = {Knabner, Peter}, faupublication = {yes}, journal = {The Preprint-Series of the Institute of Applied Mathematics}, peerreviewed = {No}, title = {{Open} {Questions} and {Research} {Directions} in {Parameter} {Identification} for {Multicomponent} {Reactive} {Transport} in {Porous} {Media}}, volume = {315}, year = {2007} } @article{faucris.205336232, abstract = {The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of transport-reaction-diffusion equations, which is able to include macroscopic flow properties in addition to the usual exchange between arteries, veins, and tissues. For this system we propose an inverse problem of estimating all relevant parameters from PET data. We interpret the parameter identification as a nonlinear inverse problem, for which we formulate and analyze variational regularization approaches. For the numerical solution we employ gradient-based methods and appropriate splitting methods, which are used to investigate some test cases.}, author = {Reips, Louise and Burger, Martin and Engbers, Ralf}, doi = {10.1515/jiip-2015-0016}, faupublication = {no}, journal = {Journal of Inverse and Ill-posed Problems}, keywords = {Parameter identification;dynamic PET;inverse problems;image processing;forward-backward splitting;reaction;diffusion;transport}, pages = {185-200}, peerreviewed = {Yes}, title = {{Towards} dynamic {PET} reconstruction under flow conditions: {Parameter} identification in a {PDE} model}, volume = {26}, year = {2018} } @article{faucris.110901824, abstract = {Inverse methods are increasingly used to estimate the hydraulic properties of unsaturated soils. The method generally uses a weighted least-squares approach in which numerically simulated data are fitted to measured data. In this study we used inverse methods to estimate the unsaturated soil hydraulic properties from continuous and multi step column outflow experiments. The method employs piecewise polynomial functions to obtain a free-form parameterization of the hydraulic properties, rather than fixed functional forms typical of the van Gen-uchten-Mualem and Brooks-Corey-Burdine models. For the polynomial functions we used quadratic B-splines and piecewise cubic Hermite interpolation. The method leads to local parameterizations that can also be hierarchic, depending on the invoked number of degrees of freedom. Since a suitable number of degrees of freedom cannot be defined a priori, we embedded the estimation method into a multilevel procedure, which also included a stability analysis, based on singular value decomposition of the sensitivity matrix. The optimization procedure was made more stable by imposing monotonicity constraints on the hydraulic functions. Tests with synthetic and measured data from column outflow experiments show the validity and robustness of the method. © Soil Science Society of America.}, author = {Bitterlich, Sandro and Durner, Wolfgang and Iden, Sascha and Knabner, Peter}, doi = {10.2113/3.3.971}, faupublication = {yes}, journal = {Vadose Zone Journal}, pages = {971-981}, peerreviewed = {Yes}, title = {{Inverse} estimation of the unsaturated soil hydraulic properties from column outflow experiments using free-form parameterizations}, volume = {3}, year = {2004} } @incollection{faucris.122724844, author = {Knabner, Peter and Frolkovic, Peter}, booktitle = {Computational Methods in Water Resources}, faupublication = {yes}, pages = {93–100}, peerreviewed = {unknown}, publisher = {Computational Mechanics Publication, Southampton}, title = {{Consistent} {Velocity} {Approximations} in {Finite} {Element} or {Volume} {Discretizations} of {Density} {Driven} {Flow}}, url = {http://www.mso.math.fau.de/fileadmin/am1/users/knabner/publicationen/ConsVelApproxDensFlow_CompMethWR_96.pdf}, volume = {1}, year = {1996} } @article{faucris.111347544, abstract = {The conjugate gradient boundary iteration (CGBI) is a domain decomposition method for elliptic partial differential equations. In the context of fractional step methods [7], a Navier-Stokes solver based on CGBI [1],[2],[3],[5] and a characteristic's method [5] is constructed. Numerical results for the flow around a cylinder (modelled in 2d) are presented.}, author = {Kräutle, Serge and Wielage, Kerstin}, doi = {10.1016/S0362-546X(01)00536-3}, faupublication = {yes}, journal = {Nonlinear Analysis - Theory Methods & Applications}, pages = {4193-4203}, peerreviewed = {Yes}, title = {{The} {CGBI} method for viscous channel flows and its preconditioning}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X01005363}, volume = {47}, year = {2001} } @article{faucris.123685144, abstract = {In this paper we present and investigate a stochastic model and its associated Fokker-Planck equation for the lay-down of fibers on a conveyor belt in the production process of nonwoven materials. The model is based on a stochastic differential equation taking into account the motion of the fiber under the influence of turbulence. A reformulation as a stochastic Hamiltonian system and an application of the stochastic averaging theorem lead to further simplifications of the model. Finally, the model is used to compute the distribution of functionals of the process that are important for the quality assessment of industrial fabrics. © 2007 Society for Industrial and Applied Mathematics.}, author = {Götz, Thomas and Klar, Axel and Marheineke, Nicole and Wegener, Raimund}, doi = {10.1137/06067715X}, faupublication = {no}, journal = {SIAM Journal on Applied Mathematics}, keywords = {Fiber dynamics; Fokker-planck equations; Stochastic averaging; Stochastic hamiltonian system}, pages = {1704-1717}, peerreviewed = {Yes}, title = {{A} stochastic model and associated {Fokker}-{Planck} equation for the fiber lay-down process in nonwoven production processes}, volume = {67}, year = {2007} } @article{faucris.116635904, abstract = {This work deals with the behavior of viscoelastic jets under gravitational forces described by an asymptotic upper convected Maxwell (UCM) model, system of partial differential equations. Considering fiber spinning, we show that the one-dimensional model equations in general allow for the simulation of drawing processes with and without die swell effect. But, as the model is of hyperbolic type and the run of the characteristics crucially depend on the physical parameters, the existence regimes of the stationary solutions associated to certain boundary conditions turn out to be limited. We investigate the regimes for gravitational uniaxial and 2d spinning scenarios numerically.}, author = {Marheineke, Nicole and Lorenz, Maike and Wegener, Raimund}, doi = {10.1186/2190-5983-4-2}, faupublication = {yes}, journal = {Journal of Mathematics in Industry}, keywords = {boundary value problem; die swell; existence of solutions; fiber spinning; nonlinear viscoelasticity; UCM fluid}, peerreviewed = {unknown}, title = {{On} simulations of spinning processes with a stationary one-dimensional upper convected {Maxwell} model}, volume = {4}, year = {2014} } @masterthesis{faucris.209590658, author = {Prechtel, Alexander}, faupublication = {no}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Die} {Schätzung} von {Variogrammen} durch {Betrachtung} ihrer {Integrale}}, year = {1997} } @article{faucris.121950224, abstract = {This paper presents a slender body theory for the dynamics of a curved inertial viscous Newtonian fiber. Neglecting surface tension and temperature dependence, the fiber flow is modeled as a three-dimensional free boundary value problem in terms of instationary incompressible Navier-Stokes equations. From regular asymptotic expansions in powers of the slenderness parameter, leading-order balance laws for mass (cross-section) and momentum are derived that combine the unrestricted motion of the fiber centerline with the inner viscous transport. The physically reasonable form of the one-dimensional fiber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms. For the numerical investigation of the viscous, gravitational and rotational effects on the fiber dynamics, a finite volume approach on a staggered grid with implicit upwind flux discretization is applied. Copyright © 2007 John Wiley & Sons, Ltd.}, author = {Panda, Satyananda and Marheineke, Nicole and Wegener, Raimund}, doi = {10.1002/mma.962}, faupublication = {no}, journal = {Mathematical Methods in the Applied Sciences}, keywords = {Asymptotic expansions; Curved viscous fibers; Free boundary value problem; Navier-stokes equations; Slender body theory}, pages = {1153-1173}, peerreviewed = {Yes}, title = {{Systematic} derivation of an asymptotic model for the dynamics of curved viscous fibers}, volume = {31}, year = {2008} } @article{faucris.122619024, abstract = {This article deals with the determination of nonlinear coefficient functions in partial differential equations in the field of soil science. We consider two examples to illustrate the numerical determination of nonlinear coefficient functions. In detail, these are the determination of the sorption characteristic of a chemical and the determination of the unsaturated hydraulic properties of a porous medium from measurements obtained from suitable column experiments. This inverse problem is treated by minimizing a least square functional. To cope with the ill-posedness, we apply a parametrization of the unknown nonlinear coefficient function, which is defined by an appropriate interpolation. The parametrization does not use a priori assumptions, which are not justified by physical properties. This kind of parametrization permits a hierarchical approach in the number of the degrees of freedom used. According to the hierarchical structure, we integrate the determination of the coefficient functions into a multi-level procedure. The investigation of the stability of the parametrization is based on the singular values of the sensitivity matrix.}, author = {Bitterlich, Sandro and Knabner, Peter}, doi = {10.1080/10682760310001597482}, faupublication = {yes}, journal = {Inverse Problems in Science and Engineering}, keywords = {Multi-level identification; Sorption characteristics; Stability analysis; Unsaturated hydraulic properties}, pages = {361-378}, peerreviewed = {Yes}, title = {{Numerical} methods for the determination of material properties in soil science}, volume = {12}, year = {2004} } @article{faucris.122012264, author = {Grün, Günther and Giacomelli, Lorenzo}, faupublication = {yes}, journal = {Interfaces and Free Boundaries}, pages = {111-129}, peerreviewed = {Yes}, title = {{Lower} bounds on waiting time for degenerate parabolic equations and systems}, volume = {8}, year = {2006} } @article{faucris.123796244, abstract = {Evolution equations for probability density functions (PDFs) and filtered density functions (FDFs) of random species concentrations weighted by conserved scalars are formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. This approach provides consistent numerical PDF/FDF solutions, given by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. The solutions are obtained by a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. The general FDF approach and the GRW numerical solution are illustrated for a reduced complexity problem consisting of the transport of a single scalar in groundwater. Randomness is induced by the stochastic parameterization of the hydraulic conductivity, characterized by short range correlations and small variance. The objective is to infer the statistics of the random concentration sampled at the plume center of mass, integrated over the transverse dimension of a two-dimensional spatial domain. The PDF/FDF problem can therefore be formulated in a two-dimensional domain as well, a spatial dimension and one in the concentration space. The upscaled drift and diffusion coefficients describing the PDF transport in the physical space are estimated on single-trajectories of diffusion in velocity fields with short-range correlations, owing to their self-averaging property. The mixing coefficients describing the PDF transport in concentration spaces are parameterized by the trend and the noise inferred from the statistical analysis of an ensemble of simulated concentration time series, as well as by classical mixing models. A Gaussian spatial filter applied to a Kraichnan velocity field generator is used to construct coarse-grained simulations (CGS) for FDF problems. The purposes of the CGS simulations are two-fold: first to understand the significance of the FDF approach from a practical point of view and its relation to the PDF approach; second to investigate the limits of the mixing models considered here and the desirable features of the mixing models for groundwater systems.}, author = {Suciu, Nicolae and Schüler, Lennart and Attinger, Sabine and Knabner, Peter}, doi = {10.1016/j.advwatres.2016.02.016}, faupublication = {yes}, journal = {Advances in Water Resources}, keywords = {Global random walk; Groundwater; Mixing; PDF/FDF methods}, pages = {83-98}, peerreviewed = {Yes}, title = {{Towards} a filtered density function approach for reactive transport in groundwater}, volume = {90}, year = {2016} } @article{faucris.116456824, author = {Grün, Günther and Garcke, Harald and Dal Passo, Roberta}, faupublication = {no}, journal = {SIAM Journal on Mathematical Analysis}, pages = {321-342}, peerreviewed = {Yes}, title = {{On} a fourth order degenerate parabolic equation: gobal entropy estimates and qualitative behavior of solutions}, volume = {29}, year = {1998} } @book{faucris.117985164, abstract = {Dieses Lehrbuch bietet eine lebendige und anschauliche Einführung in die mathematische Modellierung von Phänomenen aus den Natur- und Ingenieurwissenschaften. Die Leserin und der Leser lernen mathematische Modelle zu verstehen und selbst herzuleiten und finden gleichzeitig eine Fülle von wichtigen Beispielen für die im Mathematikstudium behandelten abstrakten Konzepte.

Es werden Methoden aus der Linearen Algebra, der Analysis und der Theorie der gewöhnlichen und partiellen Differentialgleichungen benutzt bzw. sorgfältig eingeführt. Anwendungsbeispiele aus den Bereichen elektrische Netzwerke, chemische Reaktionskinetik, Populationsdynamik, Strömungsdynamik, Elastizitätstheorie und Kristallwachstum werden ausführlich behandelt. Der Stoffumfang des Buches eignet sich für bis zu zwei vierstündige Vorlesungen für Studierende der Mathematik und der Ingenieur- oder Naturwissenschaften ab dem vierten Semester.}, address = {Berlin Heidelberg}, author = {Eck, Christof and Garcke, Harald and Knabner, Peter}, doi = {10.1007/978-3-642-18424-6}, edition = {2}, faupublication = {yes}, isbn = {978-3-642-18423-9}, peerreviewed = {unknown}, publisher = {Springer}, series = {Springer-Lehrbuch}, title = {{Mathematische} {Modellierung}}, url = {http://www.springer.com/de/book/9783642184239#aboutBook}, year = {2011} } @article{faucris.117796624, abstract = {The variance of the advection-diffusion processes with variable coefficients is exactly decomposed as a sum of dispersion terms and memory terms consisting of correlations between velocity and initial positions. For random initial conditions, the memory terms quantify the departure of the preasymptotic variance from the time-linear diffusive behavior. For deterministic initial conditions, the memory terms account for the memory of the initial positions of the diffusing particles. Numerical simulations based on a global random walk algorithm show that the influence of the initial distribution of the cloud of particles is felt over hundreds of dimensionless times. In case of diffusion in random velocity fields with finite correlation range the particles forget the initial positions in the long-time limit and the variance is self-averaging, with clear tendency toward normal diffusion. © 2009 The American Physical Society.}, author = {Suciu, Nicolae and Vamo̧s, Cǎlin and Radu, Adrian Florin and Vereecken, Harry and Knabner, Peter}, doi = {10.1103/PhysRevE.80.061134}, faupublication = {yes}, journal = {Physical Review E}, peerreviewed = {Yes}, title = {{Persistent} memory of diffusing particles}, volume = {80}, year = {2009} } @article{faucris.123847284, abstract = {[1] In this article a systematic approach for the efficient computation of the transport and reaction of a multispecies, multireaction system is proposed. The objective of this approach is to reformulate the given system of differential or differential-algebraic equations in such a way that the couplings and the nonlinearities are concentrated in a reduced number of equations (if compared to the original formulation), while some linear equations decouple from the system. The resulting system is handled in the spirit of a global implicit approach ("one step method") avoiding operator splitting techniques. The reduction of the problem size proposed in this article helps to limit the large computational costs of numerical simulations for such problems. The reduction mechanism is a generalization of the method proposed in a previous paper. Now, problems with mixed mobile/immobile species, homogeneous/heterogeneous kinetic/equilibrium reactions are considered, while the previous publication was restricted to problems without heterogeneous equilibrium reactions (such as equilibrium sorption). An application of the reduction mechanism to an example problem is given in order to investigate the reduction of the number of coupled nonlinear equations and to compare it to other methods. Copyright 2007 by the American Geophysical Union.}, author = {Kräutle, Serge and Knabner, Peter}, doi = {10.1029/2005WR004465}, faupublication = {yes}, journal = {Water Resources Research}, peerreviewed = {Yes}, title = {{A} reduction scheme for coupled multicomponent transport-reaction problems in porous media: {Generalization} to problems with heterogeneous equilibrium reactions}, volume = {43}, year = {2007} } @article{faucris.117788044, abstract = {We derive error estimates for finite element discretizations of phase field models that describe phase transitions in nonisothermal mixtures. Special attention is paid to the applicability of the result for a large class of models with nonlinear constitutive relations and to an approach that avoids an exponential dependence of the constants in the error estimate on the approximation parameter that models the thickness of the diffuse phase transition region. The main assumptions on the model are a convexity condition for a function that can be interpreted as the negative local part of the entropy of the system, a suitable regularity of the exact solutions, and a spectrum estimate for the operator of the Allen-Cahn equation. The spectrum estimate is crucial to avoid the exponential dependence of error constants on the approximation parameters in the model. This is done by a technique introduced in [X. Feng and A. Prohl, Math. Comp., 73 (2004), pp. 541-567] for phase transitions of pure materials with linear constitutive relations. © 2010 Society for Industrial and Applied Mathematics.}, author = {Eck, Christof and Jadamba, Baasansuren and Knabner, Peter}, doi = {10.1137/050637984}, faupublication = {yes}, journal = {SIAM Journal on Numerical Analysis}, keywords = {A priori error estimate; Finite element method; Phase field model; Thermodynamically consistent model}, pages = {4429-4445}, peerreviewed = {Yes}, title = {{Error} estimates for a finite element discretization of a phase field model for mixtures}, volume = {47}, year = {2010} } @incollection{faucris.116680564, author = {Lorenz, Maike and Marheineke, Nicole and Wegener, Raimund}, booktitle = {Progress in Industrial Mathematics at ECMI 2012}, faupublication = {yes}, pages = {91-98}, peerreviewed = {unknown}, publisher = {Springer}, title = {{On} viscoelastic fiber spinning: {Die} swell effect in 1d uniaxial {UCM} model}, year = {2014} } @article{faucris.117798824, author = {Knabner, Peter and Mikelic, Andro and Pop, Iuliu Sorin}, doi = {10.1007/s10596-013-9348-0}, faupublication = {yes}, journal = {Computational Geosciences}, pages = {443-445}, peerreviewed = {Yes}, title = {{Special} issue "{Mathematics} of {Porous} {Media}," dedicated to {Professor} {C}.{J}. van {Duijn} on the occasion of his 60th anniversary}, volume = {17}, year = {2013} } @article{faucris.213920002, abstract = {In this article, we derive an effective model for biofilm growth in a saturated porous medium. Several experimental investigations found out that biomass is in general very heterogeneous and contains in particular channels filled with fluid. These channels facilitate the transport of nutritive substances within the biofilm by advection. Referring to this, we model the biofilm itself at the pore-scale as a porous medium. Hence the starting point at the pore-scale is a Darcy-Stokes system, where the Beavers-Joseph boundary condition at the corresponding interface is proposed. By formal periodic homogenization we derive an averaged model describing the process via Darcy's law and upscaled transport equations with effective coefficients given by the evolving microstructure. Based on the assumption of uniform evolve of the underlying pore geometry, solvability in a weak sense global in time or at least up to a possible clogging phenomenon is stated.}, author = {Schulz, Raphael}, doi = {10.1002/zamm.201800123}, faupublication = {yes}, journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik}, note = {CRIS-Team WoS Importer:2019-03-20}, peerreviewed = {Yes}, title = {{Biofilm} modeling in evolving porous media with {Beavers}-{Joseph} condition}, volume = {99}, year = {2019} } @article{faucris.204146981, abstract = {Mathematical models of virus dynamics have not previously acknowledged spatial resolution at the intracellular level despite substantial arguments that favor the consideration of intracellular spatial dependence. The replication of the hepatitis C virus (HCV) viral RNA (vRNA) occurs within special replication complexes formed from membranes derived from endoplasmatic reticulum (ER). These regions, termed membranous webs, are generated primarily through specific interactions between nonstructural virus-encoded proteins (NSPs) and host cellular factors. The NSPs are responsible for the replication of the vRNA and their movement is restricted to the ER surface. Therefore, in this study we developed fully spatio-temporal resolved models of the vRNA replication cycle of HCV. Our simulations are performed upon realistic reconstructed cell structuresnamely the ER surface and the membranous websbased on data derived from immunostained cells replicating HCV vRNA. We visualized 3D simulations that reproduced dynamics resulting from interplay of the different components of our models (vRNA, NSPs, and a host factor), and we present an evaluation of the concentrations for the components within different regions of the cell. Thus far, our model is restricted to an internal portion of a hepatocyte and is qualitative more than quantitative. For a quantitative adaption to complete cells, various additional parameters will have to be determined through further in vitro cell biology experiments, which can be stimulated by the results described in the present study.}, author = {Knodel, Markus and et al.}, author_hint = {Knodel MM, Reiter S, Targett-Adams P, Grillo A, Herrmann E, Wittum G}, doi = {10.3390/v9100282}, faupublication = {no}, journal = {Viruses-Basel}, keywords = {computational virology;hepatitis C virus (HCV);viral dynamics;within-host viral modelling;mathematical models of viral RNA cycle;3D spatio-temporal resolved mathematical models;realistic geometries;(surface) partial differential equations;Finite Volumes;massively parallel multigrid solvers}, peerreviewed = {Yes}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{3D} {Spatially} {Resolved} {Models} of the {Intracellular} {Dynamics} of the {Hepatitis} {C} {Genome} {Replication} {Cycle}}, volume = {9}, year = {2017} }