A Fokker-Planck approach for probability distributions of species concentrations transported in heterogeneous media

Suciu N, Radu AF, Attinger S, Schüler L, Knabner P (2015)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2015

Journal

Journal of Computational and Applied Mathematics Elsevier

Publisher: Elsevier

Book Volume: 289

Pages Range: 241-252

Article Number: 9984

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_SuciuRaduAttingerSchuelerKn_AFokkerPlanckApproachForProbabDistrOfSpecConcTransInHetrogeneousMedia

DOI: 10.1016/j.cam.2015.01.030

Abstract

Abstract We identify sufficient conditions under which evolution equations for probability density functions (PDF) of random concentrations are equivalent to Fokker-Planck equations. The novelty of our approach is that it allows consistent PDF approximations by densities of computational particles governed by Itô processes in concentration-position spaces. Accurate numerical solutions are obtained with a global random walk (GRW) algorithm, stable, free of numerical diffusion, and insensitive to the increase of the total number of computational particles. The system of Itô equations is specified by drift and diffusion coefficients describing the PDF transport in the physical space, provided by up-scaling procedures, as well as by drift and mixing coefficients describing the PDF transport in concentration spaces. Mixing models can be obtained similarly to classical PDF approaches or, alternatively, from measured or simulated concentration time series. We compare their performance for a GRW-PDF numerical solution to a problem of contaminant transport in heterogeneous groundwater systems.

Authors with CRIS profile

Nicolae Suciu Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Friedrich-Schiller-Universität Jena DE Germany (DE) University of Bergen / Universitetet i Bergen NO Norway (NO)

How to cite

APA:

Suciu, N., Radu, A.F., Attinger, S., Schüler, L., & Knabner, P. (2015). A Fokker-Planck approach for probability distributions of species concentrations transported in heterogeneous media. Journal of Computational and Applied Mathematics, 289, 241-252. https://doi.org/10.1016/j.cam.2015.01.030

MLA:

Suciu, Nicolae, et al. "A Fokker-Planck approach for probability distributions of species concentrations transported in heterogeneous media." Journal of Computational and Applied Mathematics 289 (2015): 241-252.

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