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Title (Primary) A Fokker–Planck approach for probability distributions of species concentrations transported in heterogeneous media
Author Suciu, N.; Radu, F.A.; Attinger, S.; Schüler, L.; Knabner, P.;
Journal Journal of Computational and Applied Mathematics
Year 2015
Department CHS;
Volume 289
Language englisch;
POF III (all) T53;
Keywords PDF methods; Mixing; Random walk; Porous media
UFZ wide themes RU5;
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.
ID 16350
Persistent UFZ Identifier http://www.ufz.de/index.php?en=20939&ufzPublicationIdentifier=16350
Suciu, N., Radu, F.A., Attinger, S., Schüler, L., Knabner, P. (2015):
A Fokker–Planck approach for probability distributions of species concentrations transported in heterogeneous media
J. Comput. Appl. Math. 289 , 241 - 252