2d simulations of interfacial instabilities at deformable single doplets - Bäumler, Kathrin; Wegener, Mirco; Bänsch, Eberhard; Paschedag, Anja (Proceedings of the Seventh International Conference on CFD in the Minerals and Process Industries, CSIRO, 2009)
In liquid/liquid extraction processes, e.g. in ternary systems, where the transfer of a solute between a dispersed and a continuous phase is considered, reliable predictions of mass transfer coefficients and retention times are indispensable. Especially in the case, where interfacial instabilities like drop deformation and Marangoni-convection occur, th e influencing factors and their quantitative nature are not yet fully understood. In our numerical model we consider a Newtonian viscous two phase flow, representing a single deformable drop. Simulations are performed using the academic code NAVIER, which features a sharp interface model and a variational formulation of the curvature. This approach provides an effective method for a consistent, very exact description of discrete surface stresses. Results of drop rise velocitie s and mass transfer rates in the 2D case of spherical as well as deformable drops are presented (diameters varying from 1 mm to 5 mm) . The simulations are compared to experimental results in the system water/toluene and to numerical results of non- deformable drops obtained by STAR-CD. Especially with the onset of drop deformation, the system is excellently reflected by the simulations, i.e. the terminal velocities calculated with NAVIER show a deviation of no more than 4% to the experimental results.

A Coarsening Finite Element Strategy in Image Selective Smoothing - Bänsch, Eberhard; Mikula, Karol (Computing and Visualization in Science, 1997)
We introduce the coarsening of finite element computational grid strategy into the method proposed by Kačur and Mikula in [11] for the numerical solution of the Perona-Malik model modified in the sense of Catté, Lions, Morel and Coll. It improves the efficiency of the method, while the solution tends to be more flat during the selective smoothing process applied to the image. The numerical approximation consists of Rothe's method in time and linear finite elements on unstructured adaptively coarsened meshes in space. © Springer-Verlag 1997.
UnivIS-Import:2015-03-05:Pub.1997.nat.dma.lama3.acoars

A comparison of several time discretization methods for free surface flows - Bänsch, Eberhard; Weller, Stephan (ALGORITMY 2012, 19th Conference on Scientific Computing, 2012)
The fundamental problems in the numerical approximation of multiphase systems, or more generally speaking, in the treatment of flows with capillary free boundaries are the representation of the free surface, evaluating the curvature, handling of discontinuities, most importantly the pressure jump, and time discretization strategies for the decoupling of flow computation and geometry. While for the first three items there exists a vast literature and many techniques developed over the last two decades, the last problem of how to efficiently treat the time discretization has been widely ignored. The majority of the existing approaches just decouple the flow field from the geometry by a simple segregated approach, i.e. evaluating the geometric quantities from the previous time step. These strategy leads to a) a severe capillary CFL condition and b) is of first order in time at most. Existing semi-implicit discretizations exist that overcome problem a), but are still first order only and rather dissipative in certain situations.We compare different existing time discretization schemes for the fully coupled system of Navier-Stokes and the phase boundary condition. Time discretization might be semi-implicit, fully implicit or linearly implicit. The methods are applied to a simple test case where experimental order of convergence and numerical dissipation can be compared relatively easily.

Adaptive Finite Elements for Exterior Domain Problems - Bänsch, Eberhard; Dörfler, Willy (Numerische Mathematik, 1998)
We present an adaptive finite element method for solving elliptic problems in exterior domains, that is for problems in the exterior of a bounded closed domain in ℝd, d ∈ 2,3. We describe a procedure to generate a sequence of bounded computational domains Ωkh, k = 1, 2, ..., more precisely, a sequence of successively finer and larger grids, until the desired accuracy of the solution uh is reached. To this end we prove an a posteriori error estimate for the error on the unbounded domain in the energy norm by means of a residual based error estimator. Furthermore we prove convergence of the adaptive algorithm. Numerical examples show the optimal order of convergence.
UnivIS-Import:2015-03-05:Pub.1998.nat.dma.lama3.adapti

Adaptive Finite-Element Techniques for Navier-Stokes Equations and other Transient Problems - Bänsch, Eberhard (Adaptive Finite and Boundary Element Methods, 1993)
UnivIS-Import:2015-04-20:Pub.1993.nat.dma.lama3.adapti

Adaptivity in 3D Image Processing - Bänsch, Eberhard; Mikula, Karol (Computing and Visualization in Science, 2001)
We present an adaptive numerical scheme for computing the nonlinear partial differential equations arising in 3D imagemultiscale analysis. The scheme is based on a semiimplicit scale discretization and on an adaptive finite element method in 3D-space. Successive coarsening of the computational grid is used for increasing the efficiency of the numerical procedure. L∞-stability of the semi-discrete scheme is proved and computational results related to 3D nonlinear image filtering are discussed. © 2001 Springer-Verlag.
UnivIS-Import:2015-03-09:Pub.2001.nat.dma.lama3.adapti

A Finite Element Method for Dendritic Growth - Bänsch, Eberhard; Schmidt, Alfred (Computational Crystal Growers Workshop, 1992)
UnivIS-Import:2015-04-16:Pub.1992.nat.dma.lama3.afinit

A Finite Element Method for Surface Diffusion: the Parametric Case - Bänsch, Eberhard; Morin, Pedro; Nochetto, Ricardo (Journal of Computational Physics, 2005)
Surface diffusion is a (fourth order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for parametric surfaces with or without boundaries. The method is semi-implicit, requires no explicit parametrization, and yields a linear system of elliptic PDE to solve at each time step. We next develop a finite element method, propose a Schur complement approach to solve the resulting linear systems, and show several significant simulations, some with pinch-off in finite time. We introduce a mesh regularization algorithm, which helps prevent mesh distortion, and discuss the use of time and space adaptivity to increase accuracy while reducing complexity. © 2004 Elsevier Inc. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2005.nat.dma.lama3.afinit
Keywords: Finite elements; Fourth-order parabolic problem; Pinch-off; Schur complement; Smoothing effect; Surface diffusion

A finite element pressure correction scheme for the Navier-Stokes equations with traction boundary condition - Bänsch, Eberhard (Computer Methods in Applied Mechanics and Engineering, 2014)
We consider the popular pressure correction scheme for the solution of the time dependent Navier–Stokes equations with traction boundary condition. A finite element based method to improve the performance of the classical approach is proposed. The improvement is achieved by modifying the traction boundary condition for the provisional velocity <a class="mathImg" data-mathurl="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0045782514002163&_mathId=si44.gif&_user=111111111&_pii=S0045782514002163&_rdoc=1&_issn=00457825&md5=ef08b15511136a17f8140dfe881f5933" title="View the MathML source"><img alt="View the MathML source" class="imgLazyJSB inlineImage" data-inlimgeid="1-s2.0-S0045782514002163-si44.gif" data-loaded="true" height="13" src="http://ars.els-cdn.com/content/image/1-s2.0-S0045782514002163-si44.gif" style="margin-top: -5px; vertical-align: middle; display: inline;" title="View the MathML source" width="29" /><mover accent="true">ũ</mover>n+1 in each time step. The corresponding term consists of a simple boundary functional involving the normal derivative of the pressure correction that can be evaluated in a natural and easy way in the context of finite elements. Computational results show a significant improvement of the solution, in particular for the pressure in the case of smooth domains.
Keywords: Navier–Stokes equations; Traction boundary condition; Open boundary condition; Pressure correction; Finite elements

A mixed finite element method for elliptic operators with Wentzell boundary condition - Bänsch, Eberhard; Gahn, Markus (IMA Journal of Numerical Analysis, 2018)

A model for two phase flow with evaporation - Krahl, Rolf; Adamov, Miroslav; Lozano Avilés, Miriam; Bänsch, Eberhard (Proceedings of 3rd International Symposium on Two-Phase Flow Modelling and Experimentation, 2004)

An Adaptive Finite-Element-Strategy for the Three-Dimensional Time-Dependent Navier-Stokes Equations - Bänsch, Eberhard (Journal of Computational and Applied Mathematics, 1991)
An adaptive strategy for three-dimensional time-dependent problems in the context of the FEM is presented. The basic tools are a mechanism for local refinement and coarsening of simplicial meshes and an unexpensive error-estimator. The algorithm for local grid modification is based on bisecting tetrahedra. The method is applied to the Navier-Stokes equations. © 1991.
UnivIS-Import:2015-03-05:Pub.1991.nat.dma.lama3.anadap
Keywords: Adaptivity; local mesh refinement; Navier-Stokes equations

An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition - Bänsch, Eberhard; Morin, Pedro; Nochetto, Ricardo (SIAM Journal on Numerical Analysis, 2002)
We introduce and study an adaptive finite element method (FEM) for the Stokes system based on an Uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity. We show linear convergence in terms of the outer iteration counter for the pairs of spaces consisting of continuous finite elements of degree k for velocity, whereas for pressure the elements can be either discontinuous of degree k - 1 or continuous of degree k -1 and k. The popular Taylor-Hood family is the sole example of stable elements included in the theory, which in turn relies on the stability of the continuous problem and thus makes no use of the discrete inf-sup condition. We discuss the realization and complexity of the elliptic adaptive inner solver and provide consistent computational evidence that the resulting meshes are quasi-optimal.
UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama3.anadap
Keywords: A posteriori error estimators; Adaptive mesh refinement; Convergence; Data oscillation; Performance; Quasi-optimal meshes

An Operator-Splitting Finite-Element Approach to an 8:1 Thermal Cavity Problem - Bänsch, Eberhard; Davis, Dominic (International Journal For Numerical Methods in Fluids, 2002)
This article describes the methodology for, and results obtained from, our contribution to the thermalcavity benchmark test. Our solutions were obtained on graded rectangular grids for two different time-discretization schemes by applying a finite-element procedure to the model equations, and a combination of conjugate-gradient and GMRES solvers to the resulting matrix systems. Copyright © 2002 John Wiley & Sons, Ltd.
UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama3.anoper
Keywords: Advection; CG method; Finite element; Galerkin; GMRES; Navier-Stokes

A posteriori error control for fully discrete Crank-Nicolson schemes - Bänsch, Eberhard; Karakatsani, F.; Makridakis, Charalambos (SIAM Journal on Numerical Analysis, 2012)
We derive residual-based a posteriori error estimates of optimal order for fully discrete approximations for linear parabolic problems. The time discretization uses the Crank–Nicolson method, and the space discretization uses finite element spaces that are allowed to change in time. The main tool in our analysis is the comparison with an appropriate reconstruction of the discrete solution, which is introduced in the present paper. Read More: http://epubs.siam.org/doi/abs/10.1137/110839424

A posteriori error estimates for fully discrete schemes for the time dependent Stokes problem - Bänsch, Eberhard; Karakatsani, F.; Makridakis, Charalambos (Calcolo, 2018)
This work is devoted to a posteriori error analysis of fully discrete finite element approximations to the time dependent Stokes system. The space discretization is based on popular stable spaces, including Crouzeix-Raviart and Taylor-Hood finite element methods. Implicit Euler is applied for the time discretization. The finite element spaces are allowed to change with time steps and the projection steps include alternatives that is hoped to cope with possible numerical artifices and the loss of the discrete incompressibility of the schemes. The final estimates are of optimal order in L-infinity(L-2) for the velocity error.
Keywords: A posteriori error estimators; Time dependent Stokes; Reconstruction; Adaptivity; Mesh change; Crouzeix-Raviart element

A POSTERIORI ERROR ESTIMATES FOR PRESSURE-CORRECTION SCHEMES - Bänsch, Eberhard; Brenner, Andreas (SIAM Journal on Numerical Analysis, 2016)
A posteriori error estimates for time discretization of the incompressible Stokes equations by pressure-correction methods are presented. We rigorously prove global upper bounds for the incremental backward Euler scheme as well as for the two-step backward differential formula method (BDF2) in rotational form. Moreover, rate optimality of the estimators is stated for velocity (in the case of backward Euler and BDF2 in rotational form) and pressure (in the case of Euler). Computational experiments confirm the theoretical results.
Keywords: a posteriori error analysis; projection methods; fractional step methods; Navier-Stokes equations; BDF2; reconstruction; backward Euler

A posteriori estimates for the two-step backward differentiation formula and discrete regularity for the time-dependent Stokes equations - Bänsch, Eberhard; Brenner, Andreas (IMA Journal of Numerical Analysis, 2019)
We derive optimal order residual-based a posteriori error estimates for fully discrete finite element approximations to the time-dependent Stokes equations. The time discretization uses the two-step backward differentiation formula, and the space discretization is based on inf-sup stable pairs of finite elements, which are allowed to change with time. We show that the time error estimators are of optimal order. This proof of optimality uses time regularity of the semidiscrete (discrete in space) time-dependent Stokes equations. Computational examples are given to confirm the theoretical findings. For completeness, a priori estimates are also presented.
CRIS-Team Scopus Importer:2019-09-27
Keywords: a posteriori error analysis; BDF2; finite elements; reconstruction; Stokes equation; time-dependent

A priori error analysis for finite element approximations of the Stokes problem on dynamic meshes - Brenner, Andreas; Bänsch, Eberhard; Bause, Markus (IMA Journal of Numerical Analysis, 2014)
In this article we study finite element approximations of the time-dependent Stokes system on dynamically changing meshes. Applying the backward Euler method for time discretization we use the discrete Helmholtz or Stokes projection to evaluate the solution at time tn−1 on the new spatial mesh at time tn. The theoretical results consist of a priori error estimates that show a dependence on the time step size not better than 𝒪(1/Δt). These surprisingly pessimistic upper bounds are complemented by numerical examples giving evidence for a negative convergence rate, at least for a large range of time step sizes, and in this sense backing our theory. These observations imply that using adaptive meshes for incompressible flow problems is delicate and requires further investigation.

A subspace projection method for the implementation of interface conditions in a single-drop flow problem - Bäumler, Kathrin; Bänsch, Eberhard (Journal of Computational Physics, 2013)
We present a mesh moving method within a finite element context, where the interface conditions of a two-phase flow problem are conveniently included in suitable chosen subspaces of the general trial and testfunction spaces. A weak formulation of the two-phase flow problem including species transport is derived, where the problem specific function spaces are replaced by appropriate projections operating on standard function spaces. The transfer of the variational formulation to a finite element method is straightforward and results in one set of equations for both fluidic phases. This subspace projection method is applicable to a wide range of interfacial conditions for multiphase flow problems. The method is validated for single-drop flow problems including species transfer. Furthermore, an application to the simulation of stagnant caps is presented.

A thermodynamically consistent model for convective transport in nanofluids: existence of weak solutions and fem computations - Bänsch, Eberhard (Journal of Mathematical Analysis and Applications, 2019)
We present a mathematical model for convective transport in nanofluids including thermophoretic effects that is very similar to the celebrated model of Buongiorno [4]. Our model is thermodynamically consistent and consequently an energy estimate can be shown. We propose a semi–discretization in time that fully decouples the subproblems. Also for this semi–discrete problem an energy estimate can rigorously be shown. Based on this energy estimate it is proved that solutions of the semi–discrete problem converge to a weak solution of the system. We use the time discretization to define an effective, fully discrete finite element scheme. Simulations are performed for a nanofluid flowing through a heated long pipe. Careful inspection of the computational results reveal the mechanism of enhanced cooling properties of the nanofluid compared to the base fluid: The temperature gradient at the wall reduces the concentration of particles by thermophoresis. Thus, close to the wall, the viscosity is smaller compared to the bulk leading to an enhanced convective transport in the boundary layer.
CRIS-Team Scopus Importer:2019-05-02
Keywords: Energy estimate; Finite element; Heat transfer; Nanofluid; Thermophoresis; Weak solution

Axisymmetric and 3D Calculations of Melt Flow During VCz Growth - Bänsch, Eberhard; Davis, Dominic; Langmach, Hartmut; Miller, Wolfram; et al. (Journal of Crystal Growth, 2004)
Axisymmetric and 3D calculations of melt flow have been performed for a configuration used at the vapour-pressure-controlled Czochalski growth of GaAs single crystals. Thermal boundary conditions were adapted from a global simulation of the temperature field. The axisymmetric calculations with the code NAVIER confirmed the ones previously perfomed with FIDAP™. The 3D calculations showed that the flow exhibits an asymmetric transient behaviour beyond a certain critical Reynolds number. © 2004 Elsevier B.V. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.axisym
Keywords: A1. Computer simulation; A1. Convection; A1. Heat transfer; A2. Liquid encapsulated Czochralski method

Challenges in Scientific Computing - CISC 2002 - Bänsch, Eberhard (Springer, 2003)
The conference Challenges In Scientific Computing (CISC 2002) took place from October, 2 to 5, 2002. The hosting institution was the Weierstrass Insti tute for Applied Analysis and Stochastics (WIAS) in Berlin, Germany. The main purpose of this meeting was to draw together researchers working in the fields of numerical analysis and scientific computing with a common interest in the numerical treatment and the computational solution of systems of nonlinear partial differential equations arising from applications of physical and engineering problems. The main focus of the conference was on the problem class of non linear transport/diffusion/reaction systems, chief amongst these being: the Navier-Stokes equations, semiconductor-device equations and porous media flow problems. The emphasis was on unsolved problems, challenging open questions from applications and assessing the various numerical methods used to handle them, rather than concentrate on accurate results from "solved" problems. Thanks to the participants it was an interesting meeting. The presentations stimulated exchanging ideas and lively discussions. This proceedings comprises 13 papers form the conference, ranging from numerical methods for flow problems, multigrid methods, semiconductor and microwave simulation, solution methods, finite element analysis to software aspects. This interesting conference would not have been possible without the help of the staff of the WIAS. I thank all participants, and all our supporters, especially those not onstage, for making the conference a success.
UnivIS-Import:2015-07-08:Pub.2003.nat.dma.lama3.challe

Computational Comparison Between the Taylor-Hood and the Conforming Crouzeix-Raviart Element - Bänsch, Eberhard; Krahl, Rolf (ALGORITMY 2005, 2005)

Conductivity in nonpolar media: Experimental and numerical studies on sodium AOT-hexadecane, lecithin-hexadecane and aluminum(III)-3,5-diisopropyl salicylate-hexadecane systems - Peschka, Dirk; Schmidt, Jochen; Wagner, Barbara; Bänsch, Eberhard; Münch, Andreas; Peukert, Wolfgang; Prignitz, Rodolphe (Journal of Colloid and Interface Science, 2012)
The conductivity behavior of doped hydrocarbon systems is studied by applying impedance spectroscopy. In the case of 3,5-diisopropyl salicylato aluminum (III) the charge carriers are formed by dissociation of the compound and their concentration is proportional to the square root of the solute concentration. In hydrocarbon systems that consist of micelle forming compounds (sodium AOT/lecithin) a linear dependence of charge carrier concentration on solute concentration is observed in the concentration regime where micelles are present. The conduction mechanisms are studied by numerical solution of a Poisson-Nernst-Planck system that describes the charge transport. We follow two different approaches to extract the degree of micelle dissociation from the impedance data. Firstly, by computing the response of a linear approximation of the Poisson-Nernst-Planck model, and secondly by computing the fully nonlinear response from direct numerical simulations using finite elements. For high and moderate frequencies both approaches agree very well with the experimental data. For small frequencies the response becomes nonlinear and the concept of impedance fails. Furthermore, the numerically computed values for the degree of dissociation are of the same order of magnitude as the values obtained with classical formulas, but still differ by a factor of about 1/3. The direct numerical simulation allows new insight into the conduction mechanisms for different frequency regimes. © 2012 Elsevier In
Keywords: Degree of dissociation; Direct numerical simulation; Electrochemical impedance spectroscopy; Finite element analysis; Poisson-Nernst-Planck model; Reverse micelles

Convective Transport in Nanofluids: Regularity of Solutions and Error Estimates for Finite Element Approximations - Bänsch, Eberhard; Morin, Pedro (Journal of Mathematical Fluid Mechanics, 2021)
We study the stationary version of a thermodynamically consistent variant of the Buongiorno model describing convective transport in nanofluids. Under some smallness assumptions it is proved that there exist regular solutions. Based on this regularity result, error estimates, both in the natural norm as well as in weaker norms for finite element approximations can be shown. The proofs are based on the theory developed by Caloz and Rappaz for general nonlinear, smooth problems. Computational results confirm the theoretical findings.
CRIS-Team WoS Importer:2021-04-02

Convective transport in nanofluids: The stationary problem - Bänsch, Eberhard; Faghih-Naini, Sara; Morin, Pedro (Journal of Mathematical Analysis and Applications, 2020)
We analyze the existence of solutions to the stationary problem from a mathematical model for convective transport in nanofluids including thermophoretic effects that is very similar to the celebrated model of Buongiorno [6].
CRIS-Team Scopus Importer:2020-04-28
Keywords: Energy estimate; Heat transfer; Nanofluid; Thermophoresis; Weak solution

Dependency of the Apparent Contact Angle on Nonisothermal Conditions - Krahl, Rolf; Gerstmann, Jens; Behruzi, Philipp; Bänsch, Eberhard; Dreyer, Michael E. (Physics of Fluids, 2008)
The dynamic behavior of liquids in partly filled containers is influenced to a large extend by the angle between the gas-liquid phase boundary and the solid container wall at the contact line. This contact angle in turn is influenced by nonisothermal conditions. In the case of a cold liquid meniscus spreading over a hot solid wall, the contact angle apparently becomes significantly larger. In this paper we want to establish a quantitative equation for this enlargement, both from experimental and numerical data. Our findings can be used to build a subgrid model for computations, where the resolution is not sufficient to resolve the boundary layers. This might be the case for large containers which are exposed to low accelerations and where the contact angle boundary condition determines the position of the free surface. These types of computation are performed, for example, to solve propellant management problems in launcher and satellite tanks. In this application, the knowledge of the position of the free surface is very important for the withdrawal of liquid and the calculation of heat and mass transfer. © 2008 American Institute of Physics.
UnivIS-Import:2015-04-14:Pub.2008.nat.dma.lama3.depend
Keywords: contact angle; capillary flows; contact lines; thermo-capillary flows

Efficient Image Segmentation for Detection of Dislocations in High Resolution Light Microscope Images of SiC Wafers - Karpinski, Harald; Sakwe, Aloysius; Fried, Michael J.; Bänsch, Eberhard; Wellmann, Peter (Materials Science Forum, 2011)
The determination of dislocation density and in particular the dislocation distribution in SiC wafers is of particular interest for SiC crystal growth development and production. We present an image recognition tool allowing the wafer analysis with specific needs for SiC. In the first stage of expansion, micropipes are selected and counted from SiC wafers that have been etched by KO
Keywords: image analysis; dislocations; SiC; automatic detection

Experimental and Numerical Investigation of Edge Tones - Bamberger, Andreas; Bänsch, Eberhard; Siebert, Kunibert G. (ZAMM - Zeitschrift für angewandte Mathematik und Mechanik, 2004)
We study both, by experimental and numerical means the fluid dynamical phenomenon of edge tones. Of particular interest is the verification of scaling laws relating the frequency f to given quantities, namely d, the height of the jet, w, the stand-off distance and the velocity of the jet. We conclude that the Strouhal number Sd is related to the geometrical quantities through Sd = C · (d/w)n with n ≈ 1, in contrast to some analytical treatments of the problem. The constant C of the experiment agrees within 13-15% with the result of the numerical treatment. Only a weak dependence on the Reynolds number with respect to d is observed. In general, a very good agreement of the experimental and the numerical simulations is found. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.experi
Keywords: Adaptive finite elements; Edge tones; Experimental investigation; Navier-stokes equations; Numerical methods

Finite Element Discretization of the Navier-Stokes Equations with a Free Capillary Surface - Bänsch, Eberhard (Numerische Mathematik, 2001)
The instationary Navier-Stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions. A stable finite element discretization is presented. The key idea is the treatment of the curvature terms by a variational formulation. In the context of a discontinuous in time space-time element discretization stability in (weak) energy norms can be proved. Numerical examples in 2 and 3 space dimensions are given.
UnivIS-Import:2015-03-09:Pub.2001.nat.dma.lama3.finite

Finite Element Method for Epitaxial Growth with Attachment-Detachment Kinetics - Bänsch, Eberhard; Haußer, Frank; Lakkis, Omar; Li, Bo; Voigt, Axel (Journal of Computational Physics, 2004)
An adaptive finite element method is developed for a class of free or moving boundary problems modeling island dynamics in epitaxial growth. Such problems consist of an adatom (adsorbed atom) diffusion equation on terraces of different height; boundary conditions on terrace boundaries including the kinetic asymmetry in the adatom attachment and detachment; and the normal velocity law for the motion of such boundaries determined by a two-sided flux, together with the one-dimensional "surface" diffusion. The problem is solved using two independent meshes: a two-dimensional mesh for the adatom diffusion and a one-dimensional mesh for the boundary evolution. The diffusion equation is discretized by the first-order implicit scheme in time and the linear finite element method in space. A technique of extension is used to avoid the complexity in the spatial discretization near boundaries. All the elements are marked, and the marking is updated in each time step, to trace the terrace height. The evolution of the terrace boundaries includes both the mean curvature flow and the surface diffusion. Its governing equation is solved by a semi-implicit front-tracking method using parametric finite elements. Simple adaptive techniques are employed in solving the adatom diffusion as well as the boundary motion problem. Numerical tests on pure geometrical motion, mass balance, and the stability of a growing circular island demonstrate that the method is stable, efficient, and accurate enough to simulate the growing of epitaxial islands over a sufficiently long time period. © 2003 Elsevier Inc. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.finite
Keywords: Adaptivity; Adatom diffusion; Attachment-detachment kinetics; Epitaxial growth; Finite elements; Free or moving boundary problem; Front tracking; Island dynamics; Mean curvature flow; Surface diffusion

Finite element method for epitaxial growth with thermodynamic boundary conditions - Bänsch, Eberhard; Haußer, Frank; Voigt, Axel (SIAM Journal on Scientific Computing, 2005)
We develop an adaptive finite element method for island dynamics in epitaxial growth. We study a step-flow model, which consists of an adatom (adsorbed atom) diffusion equation on terraces of different height; thermodynamic boundary conditions on terrace boundaries including anisotropic line tension; and the normal velocity law for the motion of such boundaries determined by a two-sided flux, together with the one-dimensional anisotropic "surface" diffusion (edge diffusion) of edge adatoms along the step edges. The problem is solved using independent meshes: a two-dimensional mesh for the adatom diffusion and one-dimensional meshes for the boundary evolution. A penalty method is used to incorporate the boundary conditions. The evolution of the terrace boundaries includes both the weighted/anisotropic mean curvature flow and the weighted/anisotropic edge diffusion. Its governing equation is solved by a semi-implicit front-tracking method using parametric finite elements. © 2005 Society for Industrial and Applied Mathematics.
UnivIS-Import:2015-03-09:Pub.2005.nat.dma.lama3.finite
Keywords: Adaptivity; Adatom diffusion; Epitaxial growth; Finite elements; Free or moving boundary problem; Front tracking; Gibbs-Thomson; Island dynamics; Mean curvature flow; Surface diffusion

Finite Element Methods for Surface Diffusion - Bänsch, Eberhard; Morin, Pedro; Nochetto, Ricardo (Free Boundary Problems: Theory and Applications, 2004)
UnivIS-Import:2015-04-16:Pub.2004.nat.dma.lama3.finite_7

Free boundary problems in fluids and materials - Bänsch, Eberhard; Schmidt, Alfred (Handbook of Numerical Analysis, 2019)
Free boundary problems with geometric conditions for the interfaces are typically models for situations where interfacial energies play an important role. This happens for example in microscale models of phase transitions as well as models with fluidic interfaces in various scales, all important in technical applications. We give here an overview of related aspects of models and corresponding numerical methods, and present some representative applications and results.
CRIS-Team Scopus Importer:2019-07-09
Keywords: 35K; 35Q; 53Z; 65M; 65Z; 76D; Dendrites; Finite element method; Free boundary problems; Free surface flow; Interfaces; Laser welding; Level set; Liquid bridges; Phase transitions; Surface tension; Two-phase flow

Free surface deformation and heat transfer by thermocapillary convection - Bänsch, Eberhard; Basting, Steffen; Fuhrmann, Eckhart; Dreyer, Michael (Heat and Mass Transfer, 2016)

Fully implicit time discretization for a free surface flow problem - Bänsch, Eberhard; Weller, Stephan (Proceedings in Applied Mathematics and Mechanics, 2011)
One of the challenges in the numerics of free surface flows is the coupling of the flow field to the geometry of the domain. The most simple approach is an explicit decoupling, i.e. computing the flow field with geometrical information of a prior time step and then updating the geometry. This widely used approach leads to a severe CFL condition of the type , which may prescribe infinitesimally small time step sizes in the interesting case of a small Weber number (i.e. high surface tension). A semi-implicit approach utilizing the fact that , where xk is a parametrization of the capillary boundary Γ, is also available [1]. This approach can be proven to be unconditionally stable but is of first order only. It also suffers from relatively strong numerical dissipation. We present a fully implicit approach using a backward differentiation formula to achieve a time discretization method that is of second order and only minimally dissipative. A numerical example of an oscillating drop showing very low numerical dissipation and second order convergence as well as numerical evidence for the stability of the method is presented. Since the method requires the solution of a highly nonlinear coupled system, possible preconditioners for this system are discussed, including a lower order decoupling.

Highly accurate and numerical tractable coupling of nanoparticle nucleation, growth and fluid flow - Bänsch, Eberhard; Pflug, Lukas; Schikarski, Tobias (Chemical Engineering Research & Design, 2023)
Supersaturation as the thermodynamic driving force of particulate precipitation couples the mixing of solute compounds with the solid formation consisting of nucleation and molecular growth. Because the process spans many orders of magnitude in space and time, gathering spatio-temporal information by experiments is hardly achievable. Numerical simulation of the nonlinear, non-local balance equations for mass, momentum and dispersed phase provide detailed solution information in space and time. We here introduce a novel, highly accurate and very efficient numerical formulation of the population balance equations for the dispersed phase coupled to the concentration and velocity field. We reformulate the problem in terms of a fixed-point equation solving the population balance equation along Lagrangian paths with the recently developed exact Method of Moments (eMoM, Pflug et al., 2020) coupled to the concentration field (Eulerian frame). The analytical reformulation provides the information about the full particle size distribution while the computational effort remains in the order of classical moment methods and is much less than numerical schemes approximating the full particle size distribution such as finite volume methods. Furthermore, we explore the difference between an Euler-Euler and Euler-Lagrange coupling considering moderate to large P é clet numbers for the solutes and particles. It turns out that the mean particle size as a solution of the population balance is much more sensitive to the numerical discretization of the advection term than the approximation of the number density function. Based on this finding, we eventually explore the impact of particle diffusion on the solid formation process and give guidelines, when particle diffusion should be taken into account.
CRIS-Team Scopus Importer:2023-03-24
Keywords: Computational fluid dynamics; Euler-Euler and Euler-Lagrange coupling; Fixed-Point-Reformulation; Moment methods; Nanoparticle diffusion; Nucleation and size-dependent growth; Population balance equations

Impact of Marangoni Effects on the Apparent Contact Angle - A Numerical Investigation - Krahl, Rolf; Bänsch, Eberhard (Microgravity Science and Technology, 2005)
The influence of thermocapillary stress on the shape of the gas-liquid phase boundary is investigated numerically. We consider the case of a cold liquid meniscus at a heated solid wall in the absence of gravity. An "apparent contact angle" is defined geometrically and the deviation of this apparent contact angle from the prescribed static contact angle due to thermocapillary convection is studied. We observe an enlarged apparent contact angle compared to the isothermal case. Since a fixed static contact angle is used in the computations, we emphasize that this effect does not depend on the specific model of a dynamic contact angle. © Z-Tec Publishing.
UnivIS-Import:2015-04-14:Pub.2005.nat.dma.lama3.impact

Influence of the Weissenberg number on the stability of Oldroyd kind fluids - Scurtu, Nicoleta; Bänsch, Eberhard (Asia-Pacific Journal of Chemical Engineering, 2010)

Interface reorientation of cryogenic liquids under non-isothermal boundary conditions - Kulev, Nikolai; Basting, Steffen; Bänsch, Eberhard; Dreyer, Michael (Cryogenics, 2014)
We investigate the capillary driven oscillations of the liquid–vapor interface in cryogenic systems under non-isothermal boundary conditions. The oscillations took place in a partly filled cylinder during the interface reorientation from its 1 g equilibrium position to the microgravity equilibrium position after a step reduction of gravity. The latter was achieved by dropping the experimental device in the drop tower of Bremen, providing 4.7 s of microgravity. Liquid argon (<a class="mathImg" data-mathurl="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0011227514000794&_mathId=si58.gif&_user=111111111&_pii=S0011227514000794&_rdoc=1&_issn=00112275&md5=797e1f4b8ec26b35b82db71f383040ec" title="View the MathML source"><img alt="View the MathML source" class="imgLazyJSB inlineImage" data-inlimgeid="1-s2.0-S0011227514000794-si58.gif" data-loaded="true" height="15" src="http://ars.els-cdn.com/content/image/1-s2.0-S0011227514000794-si58.gif" style="margin-top: -5px; vertical-align: middle; display: inline;" title="View the MathML source" width="96" />Tsat=87.3<mspace width="0.25em"></mspace><mtext>K</mtext> at 1013 hPa) and liquid methane (<a class="mathImg" data-mathurl="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0011227514000794&_mathId=si59.gif&_user=111111111&_pii=S0011227514000794&_rdoc=1&_issn=00112275&md5=e7cbd8fd988b972d6003a45183b33baa" title="View the MathML source"><img alt="View the MathML source" class="imgLazyJSB inlineImage" data-inlimgeid="1-s2.0-S0011227514000794-si59.gif" data-loaded="true" height="14" src="http://ars.els-cdn.com/content/image/1-s2.0-S0011227514000794-si59.gif" style="margin-top: -5px; vertical-align: middle; display: inline;" title="View the MathML source" width="105" />Tsat=111.7<mspace width="0.25em"></mspace><mtext>K</mtext> at 1013 hPa) were used as experimental liquids. Axial wall temperature gradients, corresponding to a linear increase of the wall temperature, were applied above the interface position prior to the experiments with values varying between 0.2 K/mm and 2.9 K/mm. Both liquids showed a qualitatively similar reorientation behavior. The reorientation characteristics were found to depend on the value of the applied gradient and on the material properties of the experimental liquids. Numerical simulation showed a good qualitative agreement with a previous experiment with 1.34 K/mm using liquid argon, demonstrating main characteristic features of the experiment.
Keywords: Capillary driven; Cryogenic liquid–vapor interface; Microgravity; Non-isothermal boundary condition; Contact angle

Linearly implicit time discretization for free surface problems - Bänsch, Eberhard; Weller, Stephan (Proceedings in Applied Mathematics and Mechanics, 2012)
Deeper investigation of time discretization for free surface problems is a widely neglected problem. Many existing approaches use an explicit decoupling which is only conditionally stable. Only few unconditionally stable methods are known, and known methods may suffer from too strong numerical dissipativity. They are also usually of first rder only [1, 9]. We are therefore looking for unconditionally stable, minimally dissipative methods of higher order. Linearly implicit Runge-Kutta (LIRK) methods are a class of one-step methods that require the solution of linear systems in each time step of a nonlinear system. They are well suited for discretized PDEs, e.g. parabolic problems [7]. They have been used successfully to solve the incompressible Navier-Stokes equations [5]. We suggest an adaption of these methods for free surface problems and compare different approximations to the Jacobian matrix needed for such methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Local Mesh Refinement in 2 and 3 Dimensions - Bänsch, Eberhard (IMPACT of Computing in Science and Engineering, 1991)
An algorithm for local refinement of a given conforming triangulation in 2 or 3 dimensions is presented. Proofs for the finiteness of the algorithm and stability of the obtained triangulations are given. © 1991.
UnivIS-Import:2015-03-05:Pub.1991.nat.dma.lama3.localm

Mathematical and numerical modelling of fluid flow in elastic tubes - Bänsch, Eberhard; Goncharova, Olga; Koop, Andreas; Kröner, Dietmar (Computational Science and High Performance Computing III, 2008)
The study of fluid flow inside compliant vessels, which are deformed under an action of the fluid, is important due to many biochemical and biomedical applications, e.g. the flows in blood vessels. The mathematical problem consists of the 3D Navier-Stokes equations for incompressible fluids coupled with the differential equations, which describe the displacements of the vessel wall (or elastic structure). We study the fluid flow in a tube with different types of boundaries: inflow boundary, outflow boundary and elastic wall and prescribe different boundary conditions of Dirichlet- and Neumann types on these boundaries. The velocity of the fluid on the elastic wall is given by the deformation velocity of the wall. In this publication we present the mathematical modelling for the elastic structures based on the shell theory, the simplifications for cylinder-type shells, the simplifications for arbitrary shells under special assumptions, the mathematical model of the coupled problem and some numerical results for the pressure-drop problem with cylindrical elastic structure.

Mesh Refinement in Two and Three Dimensions Calcul d'erreur a posteriori et adaptation de maillage - Bänsch, Eberhard (Calcul d'erreur a posteriori et adaptation de maillage, 1995)
UnivIS-Import:2015-04-20:Pub.1995.nat.dma.lama3.meshre

Mini-Workshop: Interface Problems in Computational Fluid Dynamics - Bänsch, Eberhard; Tobiska, Lutz; Walkington, Noel J. (Oberwolfach reports, 2005)
UnivIS-Import:2015-03-09:Pub.2005.nat.dma.lama3.miniwo

Modeling and Numerical Simulation of the Infrared Photoablation Process - Bänsch, Eberhard; Olmes, Andreas; Brand, M.; Raible, M.; Lubatschowski, Holger; Ertmer, Wolfgang; Dziuk, Gerhard (Laser-Tissue Interaction, Tissue Optics, and Laser Welding III, 1998)
UnivIS-Import:2015-04-16:Pub.1998.nat.dma.lama3.modeli

Modeling and simulation of single droplet drying in an acoustic levitator - Doß, Martin; Ray, Nadja; Bänsch, Eberhard (Drying Technology, 2023)
We present a mathematical model for the full drying process of a single protein formulation droplet taking into account the convective impact arising from its levitation by a standing ultrasound wave. Using the finite element method allows us to compute the evaporation rate directly from the fully resolved heat and mass transfer within and around the levitated droplet. We apply our model to simulate the drying kinetics of pure water and aqueous phosphoglycerate kinase (PGK) droplets under various levitation and drying conditions. Empirical data from the literature are used to validate and discuss our numerical results. The acoustic streaming turns out to accelerate not only the first but also the second drying stage. Moreover, the dehydration of the protein molecules is found to be primarily responsible for their enzymatic inactivation throughout the drying process.
CRIS-Team Scopus Importer:2023-10-20
Keywords: acoustic levitation; acoustic streaming; finite element simulation; protein denaturation; Single droplet drying

Modelling of Infrared Soft-Tissue Photoablation Process - Bänsch, Eberhard; Olmes, Andreas; Franke, H.-G.; Lubatschowski, Holger; Raible, M.; Dziuk, Gerhard; Ertmer, Wolfgang (Applied Physics B-Lasers and Optics, 1997)
The photoablation process of soft tissue with free-running infrared lasers (λ = 2.70 μm, 2.79 μm, 2.94 μm) is not well understood, in particular for temperature-dependent absorption. An evaporation model has been developed, solved by the finite-element method and compared with experimental results. Both, the ablation rates and the thermal damages can be explained by a pure vaporization process with huge influence of the temperature-dependent absorption. © Springer-Verlag 1997.
UnivIS-Import:2015-03-05:Pub.1997.nat.dma.lama3.modell

Multiscale flow simulations of dilute polymeric solutions with bead-rod chains using Brownian configuration fields - Meier, Andreas; Bänsch, Eberhard; Frank, Florian (Applied Mathematics and Computation, 2025)
We couple the momentum and mass balance equations with the bead-rod chain model (Kramers chain) to simulate non-Newtonian polymeric fluids using finite elements and the Brownian configuration field method. A suitable rod-length preserving discretization is presented, which is based on the ideas of Liu's algorithm [28] and generalized into the finite-element context. Additional details concerning the parallelization of the Brownian configuration field part of the simulation are discussed to achieve outstanding code runtimes on large computation clusters. The novel coupling enables the investigation of how the bead-rod chains influence the fluid flow. This is done with proof-of-concept simulations for the start-up shear flow and flow around a cylinder scenario in 2D that serve as a reference for future research. In the start-up shear flow scenario, the velocity overshoot effect, which is typical for polymeric fluids, is successfully demonstrated. In the more challenging flow around a cylinder scenario, we numerically confirm the viscoelastic drag reduction phenomenon by comparing the drag coefficients with a purely Newtonian Navier–Stokes solution.
CRIS-Team Scopus Importer:2024-10-18
Keywords: Bead-rod chains; Brownian configuration fields; Brownian dynamics; HPC; Multiscale; Non-Newtonian; Polymeric solutions; Viscoelastic

Novel Techniques for Void Filling in Glacier Elevation Change Data Sets - Seehaus, Thorsten; Morgenshtern, Veniamin; Hübner, Fabian; Bänsch, Eberhard; Braun, Matthias (Remote Sensing, 2020)
The increasing availability of digital elevation models (DEMs) facilitates the monitoring of glacier mass balances on local and regional scales. Geodetic glacier mass balances are obtained by differentiating DEMs. However, these computations are usually affected by voids in the derived elevation change data sets. Different approaches, using spatial statistics or interpolation techniques, were developed to account for these voids in glacier mass balance estimations. In this study, we apply novel void filling techniques, which are typically used for the reconstruction and retouche of images and photos, for the first time on elevation change maps. We selected 6210 km2 of glacier area in southeast Alaska, USA, covered by two void-free DEMs as the study site to test different inpainting methods. Different artificially voided setups were generated using manually defined voids and a correlation mask based on stereoscopic processing of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) acquisition. Three “novel” (Telea, Navier–Stokes and shearlet) as well as three “classical” (bilinear interpolation, local and global hypsometric methods) void filling approaches for glacier elevation data sets were implemented and evaluated. The hypsometric approaches showed, in general, the worst performance, leading to high average and local offsets. Telea and Navier–Stokes void filling showed an overall stable and reasonable quality. The best results are obtained for shearlet and bilinear void filling, if certain criteria are met. Considering also computational costs and feasibility, we recommend using the bilinear void filling method in glacier volume change analyses. Moreover, we propose and validate a formula to estimate the uncertainties caused by void filling in glacier volume change computations. The formula is transferable to other study sites, where no ground truth data on the void areas exist, and leads to higher accuracy of the error estimates on void-filled areas. In the spirit of reproducible research, we publish a software repository with the implementation of the novel void filling algorithms and the code reproducing the statistical analysis of the data, along with the data sets themselves.<br
Keywords: glacier mass balance; elevation change; void filling

Numerical and Stability Aspects of Non-Newtonian Fluid Flow - Bänsch, Eberhard; Scurtu, Nicoleta (Proceedings in Applied Mathematics and Mechanics, 2005)
UnivIS-Import:2015-03-09:Pub.2005.nat.dma.lama3.numeri

Numerical Experiments with Adaptivity for the Porous Medium Equation - Bänsch, Eberhard (Acta Mathematica Universitatis Comenianae, 1995)
UnivIS-Import:2015-03-05:Pub.1995.nat.dma.lama3.numeri

Numerical methods for the instationary Navier-Stokes equations with a free capillary surface - Bänsch, Eberhard (1998)

Numerical Simulation of a Silicon Floating Zone with a Free Capillary Surface - Bänsch, Eberhard; Höhn, Burkhard (Scientific Computing in Chemical Engineering II, 1999)
UnivIS-Import:2015-04-20:Pub.1999.nat.dma.lama3.numeri

Numerical Simulation of Infrared Photoablation - Bänsch, Eberhard; Olmes, Andreas; Franke, H.-G.; Raible, M.; Lubatschowski, Holger; Ertmer, Wolfgang; Dziuk, Gerhard (Laser-Tissue Interaction and Tissue Optics II, 1996)
The ablation of soft tissue with free-running infrared lasers of low intensity is a thermal evaporation process. Nevertheless, the influence of the temperature dependent optical absorption is not yet understood. A detailed model of the photoablation process has been developed which was solved by the finite element method. Ablation rates and thermal damages are calculated and compared with experimental values. It has been shown, that the influence of the temperature dependent absorption coefficient cannot be neglected.
UnivIS-Import:2015-04-16:Pub.1996.nat.dma.lama3.numeri

Numerical simulation of suspension induced rheology - Prignitz, Rodolphe; Bänsch, Eberhard (Kybernetika, 2010)

Numerical simulation of two-phase flows with heat- and mass transfer - Bänsch, Eberhard; Basting, Steffen; Krahl, Rolf (Discrete and Continuous Dynamical Systems, 2014)

NUMERICAL SIMULATION OF TWO-PHASE FLOWS WITH HEAT AND MASS TRANSFER - Bänsch, Eberhard; Krahl, Rolf; Basting, Steffen (Discrete and Continuous Dynamical Systems, 2015)
We present a finite element method for simulating complex free surface flow. The mathematical model and the numerical method take into account two-phase non-isothermal flow of an incompressible liquid and a gas phase, capillary forces at the interface of both fluids, Marangoni effects due to temperature variation of the interface and mass transport across the interface by evaporation/condensation. The method is applied to two examples from microgravity research, for which experimental data are available.
Keywords: Two-phase flow; evaporation; interface; finite elements

Numerical Solution for 5-Layer Laminate Technique to determine Saturation Solubility of a Drug in a Thin Film of Pressure Sensitive Adhesive - Bänsch, Eberhard; Lee, Geoffrey; Reismann, Simone (Pharmaceutical Development and Technology, 2014)
A numerical solution of the one-dimensional diffusion equation is presented to describe the 5-layer laminate technique for estimating the saturation solubility of a drug in a thin polymer film. The boundary and initial conditions encompass a donor layer, a separating membrane, and an acceptor layer. Alteration of the drug's partition coefficient between donor and separating membrane has little influence on drug accumulation with the acceptor. The diffusivity in the separating membrane should be high to promote a short experimental time to achieve saturation equilibrium in the acceptor layer. The essential parameter to give rapid equilibrium is the thickness of the acceptor polymer film. For values of diffusivity typical for drugs of molecular weight around 500 an acceptor layer thickness of 10 μm-20 μm is required to achieve equilibrium within less than 10 d. These simulations allow the selection of suitable experimental conditions to make the 5-layer laminate technique a viable method for routine use. © 2014 Informa Healthcare USA, Inc.
UnivIS-Import:2015-03-09:Pub.2014.nat.dchph.lphte.numeri
Keywords: Diffusion equation; Polymer; Saturation solubility; Thin film; Transdermal

Numerical study of droplet evaporation in an acoustic levitator - Bänsch, Eberhard; Götz, Michael (Physics of Fluids, 2018)
We present a finite element method for the simulation of all relevant processes of the evaporation of a liquid droplet suspended in an acoustic levitation device. The mathematical model and the numerical implementation take into account heat and mass transfer across the interface between the liquid and gaseous phase and the influence of acoustic streaming on this process, as well as the displacement and deformation of the droplet due to acoustic radiation pressure. We apply this numerical method to several theoretical and experimental examples and compare our results with the well-known d(2)-law for the evaporation of spherical droplets and with theoretical predictions for the acoustic streaming velocity. We study the influence of acoustic streaming on the distribution of water vapor and temperature in the levitation device, with special attention to the vapor distribution in the emerging toroidal vortices. We also compare the evaporation rate of a droplet with and without acoustic streaming, as well as the evaporation rates in dependence of different temperatures and sound pressure levels. Finally, a simple model of protein inactivation due to heat damage is considered and studied for different evaporation settings and their respective influence on protein damage. Published by AIP Publishing.

Numerical study of single droplet drying in an acoustic levitator before the critical point of time - Doß, Martin; Bänsch, Eberhard (Chemical Engineering Science, 2022)
When using an acoustic levitator to perform single droplet drying studies, one has to be aware of its significant impact on the heat and mass transfer. In this paper, we propose a model for the first drying stage of an acoustically levitated water droplet containing suspended solids. Both the realistic geometry of the acoustic levitator and the deformation of the levitated droplet are taken into account by our numerical simulations. Empirical data from the literature are used to validate our single droplet levitation and drying model in case of pure water and binary water-maltodextrin droplets. We found that the acoustic streaming inside the levitated droplet has a retarding effect on its critical point of time when the solute forms a solid crust at the free phase boundary. Moreover, the temperature dependence of the sound wave length turned out to have a crucial impact on the performance of the acoustic levitator.
CRIS-Team Scopus Importer:2021-10-22
Keywords: Acoustic levitation; Acoustic streaming; Free boundary problem; Single droplet drying; Suspended solids

Numerical Treatment of the Navier-Stokes Equations with Slip Boudary Condition - Bänsch, Eberhard; Höhn, Burkhard (SIAM Journal on Scientific Computing, 2000)
UnivIS-Import:2015-03-09:Pub.2000.nat.dma.lama3.numeri

On the effect of self-penalization of piezoelectric composites in topology optimization - Wein, Fabian; Kaltenbacher, Manfred; Kaltenbacher, Barbara; Leugering, Günter; Bänsch, Eberhard; Schury, Fabian (Structural and Multidisciplinary Optimization, 2011)
We investigate the occurrence of self-penalization in topology optimization problems for piezoceramicmechanical composites. Our main goal is to give physical interpretations for this phenomenon, i.e., to study the question why for various problems intermediate material values are not optimal in the absence of explicit penalization of the pseudo densities. In order to investigate this effect numerical experiments for several static and/or dynamic actuator and sensor objective functions are performed and their respective results are compared. The objective functions are mean transduction, displacement, sound power, electric potential, electric energy, energy conversion and electric power.

On the stability of an evaporating liquid surface - Krahl, Rolf; Bänsch, Eberhard (Fluid Dynamics Research, 2012)

Optimal Error Estimates for the Stokes and Navier-Stokes Equations with Slip-Boundary Condition - Bänsch, Eberhard; Deckelnick, Klaus (Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 1999)
We consider a finite element discretization by the Taylor-Hood element for the stationary Stokes and Navier-Stokes equations with slip boundary condition. The slip boundary condition is enforced pointwise for nodal values of the velocity in boundary nodes. We prove optimal error estimates in the H1 and L2 norms for the velocity and pressure respectively.
UnivIS-Import:2015-03-05:Pub.1999.nat.dma.lama3.optima
Keywords: Error estimates; Finite elements; Navier-Stokes equations; Slip boundary condition; Stokes equations

Optimization of electro-mechanical smart structures - Bänsch, Eberhard; Kaltenbacher, Manfred; Leugering, Günter; Schury, Fabian; Wein, Fabian (Constrained Optimization and Optimal Control for Partial Differential Equations, 2012)
We present topology optimization of piezoelectric loudspeakers using the SIMP method and topology gradient based methods along with analytical and numerical results.
Keywords: Topology optimization; piezoelectricity; loudspeakers

Particulate flows with the subspace projection method - Prignitz, Rodolphe; Bänsch, Eberhard (Journal of Computational Physics, 2014)
A novel finite element method for the 3d simulation of (many) particles in a Newtonian carrier liquid is presented. The methods features the celebrated one domain approach, a subspace projection method to account for the rigid body motion within the particles and operator splitting. Combined with local mesh refinement the method results in a fast and accurate, though conceptually simple to implement algorithm. Validation is achieved using the sedimentation of one particle and comparing the resulting drag coefficient with theoretical and experimental results. Furthermore, a viscometer is considered, where the effective viscosity of a particle laden fluid is compared with analytic results.

PRECONDITIONERS FOR THE DISCONTINUOUS GALERKIN TIME-STEPPING METHOD OF ARBITRARY ORDER - Bänsch, Eberhard; Basting, Steffen (Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 2017)
We develop a preconditioner for systems arising from space-time finite element discretizations of parabolic equations. The preconditioner is based on a transformation of the coupled system into block diagonal form and an efficient solution strategy for the arising 2 x 2 blocks. The suggested strategy makes use of an inexact factorization of the Schur complement of these blocks, for which uniform bounds on the condition number can be proven. The main computational effort of the preconditioner lies in solving implicit Euler-like problems, which allows for the usage of efficient standard solvers. Numerical experiments are performed to corroborate our theoretical findings.
Keywords: Finite element method; time discretization; discontinuous Galerkin; preconditioning.

Preconditioning a class of fourth order problems by operator splitting - Bänsch, Eberhard; Morin, Pedro; Nochetto, Ricardo (Numerische Mathematik, 2011)
We develop preconditioners for systems arising from finite element discretizations of parabolic problems which are fourth order in space. We consider boundary conditions which yield a natural splitting of the discretized fourth order operator into two (discrete) linear second order elliptic operators, and exploit this property in designing the preconditioners. The underlying idea is that efficient methods and software to solve second order problems with optimal computational effort are widely available. We propose symmetric and non-symmetric preconditioners, along with theory and numerical experiments. They both document crucial properties of the preconditioners as well as their practical performance. It is important to note that we neither need H s -regularity, s > 1, of the continuous problem nor quasi-uniform grids.

Quasi-Stability of the Primary Flow in a Cone and Plate Viscometer - Azerad, Pascal; Bänsch, Eberhard (Journal of Mathematical Fluid Mechanics, 2004)
We investigate the flow between a shallow rotating cone and a stationary plate. This cone and plate device is used in rheometry, haemostasis as well as in food industry to study the properties of the flow w.r.t. shear stress. Physical experiments and formal computations show that close to the apex the flow is approximately azimuthal and the shear-stress is constant within the device, the quality of the approximation being controlled essentially by the single parameter Re ε2, where Re is the Reynolds number and ε the thinness of the cone-plate gap. We establish this fact by means of rigorous energy estimates and numerical simulations. Surprisingly enough, this approximation is valid though the primary flow is not itself a solution of the Navier-Stokes equations, and it does not even fulfill the correct boundary conditions, which are in this particular case discontinuous along a line, thus not allowing for a usual Leray solution. To overcome this difficulty we construct a suitable corrector.
UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.quasis
Keywords: Asymptotic analysis; CFD; Finite elements; Flow chamber; Haemodynamics; Haemostasis; Navier-Stokes equations; Nonlinear stability; Rheometry; Rotating fluids; Shallow domains

Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flows - Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K. (SIAM Journal on Scientific Computing, 2014)

Schur preconditioning of the Stokes equations in channel-dominated domains - Meier, Andreas; Bänsch, Eberhard; Frank, Florian (Computer Methods in Applied Mechanics and Engineering, 2022)
A novel precondition operator for the Schur complement of the stationary Stokes equations is proposed. Numerical experiments demonstrate that its discrete version is superior to established precondition operators if the computational domain is a thin channel or contains such (e.g. porous media or filters). Discrete diffusion is added to the established precondition operator, which is heuristically motivated by Darcy’s law—a homogenization result of Stokes’ equations on perforated domains. As proof of concept, we embed the operator into a block-diagonal precondition matrix for MINRES and solve the stationary Stokes saddle-point system. For domains with complex geometries, the number of iterations required to meet a certain tolerance is significantly reduced. The proposed operator can easily be incorporated into an already existing numerical solver, does not change the sparsity pattern of the established precondition operator for finite element discretizations, and is in particular suitable for distributed parallel implementations.<br
Keywords: Stokes; saddle-point system; preconditioning; porous media; thin channels; digital rock

Simulation and experimental validation of magnetic nanoparticle accumulation in a bloodstream mimicking flow system - Reinelt, Magdalena; Ahlfs, Johannes; Stein, René; Alexiou, Christoph; Bänsch, Eberhard; Friedrich, Ralf P.; Lyer, Stefan; Neuß, Maria; Neuß, Nicolas (Journal of Magnetism and Magnetic Materials, 2023)
In this paper, a mathematical model for the dynamics of superparamagnetic iron oxide nanoparticles (SPIONs) in a laminar flow through a pipe under the influence of an external magnetic field of a single electromagnet is derived. The model consists of a convection–diffusion equation coupled with magnetostatic equations. The accumulation of particles along the boundary is modeled with the help of a surface concentration. Based on experimental data describing the retention of lauric acid coated SPIONs in a tubular flow under the influence of a magnetic field, the model is parametrized and finite element simulations are performed. With the exception of one outlier at low SPION concentration and high flowspeed, the simulation results agree very well with the experimental measurements within the bounds of the measurement error.
CRIS-Team Scopus Importer:2023-07-28
Keywords: Convection–diffusion equation; Finite element method (FEM); Magnetic drug targeting (MDT); Magnetic force on nanoparticles; Particle accumulation; Superparamagnetic nanoparticle (SPION)

Simulation and multi-objective optimization to improve the final shape and process efficiency of a laser-based material accumulation process - Bänsch, Eberhard; Luttmann, Andreas; Montalvo-Urquizo, Jonathan; Schmidt, Alfred; Villarreal-Marroquín, Maria G. (Journal of Mathematics in Industry, 2020)
Common goals of modern production processes are precision and efficiency. Typically, they are conflicting and cannot be optimized at the same time. Multi-objective optimization methods are able to compute a set of good parameters, from which a decision maker can make a choice for practical situations. For complex processes, the use of physical experiments and/or extensive process simulations can be too costly or even unfeasible, so the use of surrogate models based on few simulations is a good alternative. In this work, we present an integrated framework to find optimal process parameters for a laser-based material accumulation process (thermal upsetting) using a combination of meta-heuristic optimization models and finite element simulations. In order to effectively simulate the coupled system of heat equation with solid-liquid phase transitions and melt flow with capillary free surface in three space dimensions for a wide range of process parameters, we introduce a new coupled numerical 3d finite element method. We use a multi-objective optimization method based on surrogate models. Thus, with only few direct simulations necessary, we are able to select Pareto sets of process parameters which can be used to optimize three or six different performance measures.
CRIS-Team Scopus Importer:2020-02-11
Keywords: Finite element method; Free surface flow; Metamodels; Multi-objective optimization; Phase transitions; Thermal upsetting

Simulation of Dendritic Crystal Growth with Thermal Convection - Bänsch, Eberhard; Schmidt, Alfred (Interfaces and Free Boundaries, 2000)
UnivIS-Import:2015-03-09:Pub.2000.nat.dma.lama3.simula

Simulation of Industrial Crystal Growth by the Vertical Bridgman Method - Boschert, Stefan; Schmidt, Alfred; Siebert, Kunibert G.; Bänsch, Eberhard; Benz, Klaus-Werner; Dziuk, Gerhard; Kaiser, Thomas (Mathematics - Key Technology for the Future, 2003)
Single crystals of Cadmium-Zinc-Telluride are used as a substrate material for the production of infrared detectors and are usually grown by the vertical Bridgman method. We present a simulation of the whole growth process in two steps: In the first step, the (stationary) heat transport in the furnace is modeled and calculated for different positions of the ampoule. This provides information about the most important parameter during this process: the temperature distribution in furnace and ampoule. The obtained temperatures are then used in the second step as boundary conditions for the (time dependent) simulation of temperature and convection in the ampoule. Only the use of adaptive finite element methods allows an efficient numerical simulation of the moving phase boundary, the convection in the melt and the temperature distribution in melt and crystal. Numerical results are presented for both furnace and ampoule simulations.
UnivIS-Import:2015-04-20:Pub.2003.nat.dma.lama3.simula

Simulation of Instationary, Incompressible Flows - Bänsch, Eberhard (Acta Mathematica Universitatis Comenianae, 1998)
In this article a numerical method for the efficient simulation of instationary, viscous,incompressible flows in 2d and 3d is described. The time-discretization is based on the fractional step θ-scheme in a variant as an operator splitting, which was introduced in [3]
UnivIS-Import:2015-03-05:Pub.1998.nat.dma.lama3.simula

Simulations With a Thermodynamically Consistent Model for Convective Transport in Nanofluids - Bänsch, Eberhard; Faghih-Naini, Sara (Journal of Heat Transfer-Transactions of the Asme, 2021)
A nonhomogeneous model is used to simulate convective transport in nanofluids. The model is a thermodynamically consistent version of the celebrated Buongiorno model. We study two situations in detail: flow through a pipe that is heated periodically in time at one lateral wall and a lid-driven cavity with a triangular heat source placed within. Both studies reveal the mechanisms of enhanced heat transfer by nanofluids through thermophoresis: the temperature gradient at the wall leads to a reduced concentration of nanoparticles. This reduces the concentration-dependent viscosity of the suspension close to the boundary, which in turn leads to a stronger convective transport.
CRIS-Team WoS Importer:2021-11-12

Stabilization of incompressible flow problems by Riccati-based feedback - Bänsch, Eberhard; Benner, Peter (Constrained Optimization and Optimal Control for Partial Differential Equations, 2012)
We consider optimal control-based boundary feedback stabilization of flow problems for incompressible fluids. We follow an analytical approach laid out during the last years in a series of papers by Barbu, Lasiecka, Triggiani, Raymond, and others. They have shown that it is possible to stabilize perturbed flows described by Navier-Stokes equations by designing a stabilizing controller based on a corresponding linear-quadratic optimal control problem. For this purpose, algorithmic advances in solving the associated algebraic Riccati equations are needed and investigated here. The computational complexity of the new algorithms is essentially proportional to the simulation of the forward problem.
Keywords: Flow control; feedback; Navier-Stokes equations; Riccati equation

Surface Diffusion of Graphs: Variational Formulation, Error Analysis, and Simulation - Bänsch, Eberhard; Morin, Pedro; Nochetto, Ricardo (SIAM Journal on Numerical Analysis, 2004)
Surface diffusion is a (fourth-order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for graphs and derive a priori error estimates for a time-continuous finite element discretization. We also introduce a semi-implicit time discretization and a Schur complement approach to solve the resulting fully discrete, linear systems. After computational verification of the orders of convergence for polynomial degrees 1 and 2, we show several simulations in one dimension and two dimensions with and without forcing which explore the smoothing effect of surface diffusion, as well as the onset of singularities in finite time, such as infinite slopes and cracks. © 2004 Society for Industrial and Applied Mathematics.
UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.surfac
Keywords: A priori error estimates; Finite elements; Fourth-order parabolic problem; Schur complement; Smoothing effect; Surface diffusion

Taylor-Couette System with Asymmetric Boundary Conditions - Bänsch, Eberhard; Meincke, Oliver; Egbers, Christoph; Scurtu, Nicoleta (Physics of Rotating Fluids, 2000)
UnivIS-Import:2015-04-16:Pub.2000.nat.dma.lama3.taylor

The effect of mesh modification in time on the error control of fully discrete approximations for parabolic equations - Bänsch, Eberhard; Karakatsani, F.; Makridakis, Charalambos (Applied Numerical Mathematics, 2013)

Topology optimization of a piezoelectric-mechanical actuator with single- and multiple-frequency excitation - Wein, Fabian; Kaltenbacher, Manfred; Leugering, Günter; Bänsch, Eberhard; Schury, Fabian (International Journal of Applied Electromagnetics and Mechanics, 2009)
We present the topology optimization of an assembly consisting of a piezoelectric layer attached to a plate with support. The optimization domain is the piezoelectric layer. Using the SIMP (Solid Isotropic Material with Penalization) method with forced vibrations by harmonic electrical excitation, we achieve a maximization of the dynamic displacement. We show that the considered objective function can be used under certain boundary conditions to optimize the sound radiation. The vibrational patterns resulting from the optimization are analysed in comparison with the modes from an eigenvalue analysis. Multiple-frequency optimization is achieved by adaptive weighted sums. As a second optimization criterion, a flat frequency response is integrated in the optimization process.
Keywords: Topology optimization; piezoelectric coupling; sound radiation

Transient Rise Velocity and Mass Transfer of a Single Drop with Interfacial Instabilities - Wegener, Mirco; Eppinger, Thomas; Bäumler, Kathrin; Kraume, Matthias; Paschedag, Anja; Bänsch, Eberhard (Chemical Engineering Science, 2009)
Full 3D-simulations of transient interfacial mass transfer accompanied by Marangoni convection at a single spherical droplet in a quiescent liquid were performed in a moving reference coordinate system. The flow and concentration field are solved simultaneously, coupled via the additional Marangoni stress generated by concentration gradients at the interface. Fluid dynamics and mass transfer are investigated in the Marangoni convection dominated toluene/acetone/water system. The numerical results are qualitatively and quantitatively compared with own experimental results. The simulation results reveal that mass transfer is always enhanced—compared to calculations where no Marangoni convection appears—independently from the initial solute concentration. The enhancement factor of mass transfer ranges between 2 and 3.

Two- and three-dimensional transient melt-flow simulation in vapour-pressure-controlled Czochralski crystal growth - Bänsch, Eberhard; Davis, Dominic; Langmach, Hartmut; Reinhardt, Gerd; Uhle, Maria E. (Computers & Fluids, 2006)
Flow and thermal properties associated with semiconductor melt flow in an axisymmetric crucible container are studied numerically. Axisymmetric and three-dimensional computational solutions are obtained using a standard-Galerkin, finite-element solver. The crucible and crystal are optionally rotated, and the influence of gravity (through buoyancy) is accounted for via a Boussinesq approximation in the controlling Navier–Stokes equations. The results indicate a strong dependence of the flow on both rotation and buoyancy. Results for axisymmetric flows, computed with both flat and curved geometries, are presented first, and strongly suggest that rotation of crystal and crucible in the same direction (iso-rotation) is most favourable for producing a desired convexity for the crystal/melt interface. Three-dimensional results are then presented for higher Reynolds numbers, and, in particular, reveal that for iso-rotation under moderate buoyancy, the flow undergoes a switch from a steady 2D state to an unsteady 3D state, and that the temperature becomes non-trivially advected by the flow beneath the crystal. Further evidence reveals however, that on a time scale more appropriate to the crystal growth process, the (time-averaged) flow has a weaker three-dimensionality, in relation to the mean axisymmetric part, and there is only slight distortion to the temperature field beneath the crystal. A detailed examination of the instability properties is also made, revealing the underlying nonlinear mode interaction and associated frequency responses around the bifurcation point.

Uniaxial, Extensional Flows in Liquid Bridges - Bänsch, Eberhard; Berg, Christian P.; Ohlhoff, Antje (Journal of Fluid Mechanics, 2004)
In this paper we consider the possibility of generating homogeneous flows with a nearly constant strain rate. This is achieved by stretching an almost cylindrical liquid bridge under microgravity. One key issue is the adjustability of the disk diameters, necessary for maintaining ideal boundary conditions. We first study the stretching of two different fluids by both numerical and experimental means. The numerical results are compared with the experimental data and very good agreement is found. The numerical method is then used to study the behaviour of liquid bridges for quite a large range of the flow parameters (capillary number Ca and Weber number We) in order to detect those regimes with most suitable flow conditions. © 2004 Cambridge University Press.
UnivIS-Import:2015-03-09:Pub.2004.nat.dma.lama3.uniaxi

Untersuchung der Protein-Einzeltropfentrocknung in einem akustischen Levitator mit Hilfe laseroptischer Messmethoden - Perlitz, Julian; Prihoda, Felix; Bänsch, Eberhard; Lee, Geoffrey; Will, Stefan (10. ProcessNet-Jahrestagung und 34. DECHEMA-Jahrestagung der Biotechnologen 2020, 2020)

Well-posedness of an evaporation model for a spherical droplet exposed to an air flow - Bänsch, Eberhard; Doß, Martin; Gräser, Carsten; Ray, Nadja (Interfaces and Free Boundaries, 2025)
In this paper, we address the well-posedness of an evaporation model for a spherical liquid droplet taking into account the convective impact of an air flow in the ambient gas phase. From a mathematical perspective, we are dealing with a coupled ODE–PDE system for the droplet radius, the temperature distribution, and the vapor concentration. The nonlinear coupling arises from the evaporation rate modeled by the Hertz–Knudsen equation. Under physically meaningful assumptions, we prove existence and uniqueness of a weak solution until the droplet has evaporated completely. Numerical simulations are performed to illustrate how different air flows affect the evaporation process.
CRIS-Team Scopus Importer:2025-03-14
Keywords: coupled ODE–PDE system; direct numerical simulation; Hertz–Knudsen equation; nonlinear boundary condition; single droplet evaporation