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

• N. Suciu ^[1] ; F.A. Radu ^[2] ; S. Attinger ^[3] ; L. Schüler ^[3] ; P. Knabner ^[1]
  1. [1] University of Erlangen-Nuremberg

     University of Erlangen-Nuremberg

     Kreisfreie Stadt Erlangen, Alemania

     
  2. [2] University of Bergen

     University of Bergen

     Noruega

     
  3. [3] Friedrich Schiller University Jena

     Friedrich Schiller University Jena

     Kreisfreie Stadt Jena, Alemania

     

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• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 241-252
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.01.030
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• Resumen

  • 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.