Itô equation model for dispersion of solutes in heterogeneous media

Abstract

Transport processes in heterogeneous media such as ionized plasmas, natural porous media, and turbulent atmosphere are often modeled as diffusion processes in random velocity fields.
Using the Itô formalism, we decompose the second spatial moments of the concentration and the equivalent effective dispersion coefficients in terms corresponding to various physical factors which influence the transport.
We explicitly define “ergodic” dispersion coefficients, independent of the initial conditions and completely determined by local dispersion coefficients and velocity correlations. Ergodic coefficients govern an upscaled process which describes the transport at large tine-space scales. The non-ergodic behavior at finite times shown by numerical experiments for large initial plumes is explained by “memory terms” accounting for correlations between initial positions and velocity fluctuations on the trajectories of the solute molecules.

Authors

N. Suciu
Friedrich-Alexander University of Erlangen-Nuremberg, Institute of Applied Mathematics

C. Vamos
Tiberiu Popoviciu Institute of Numerical Analysis (Romanian Academy)

H. Vereecken
Research Center Julich, ICG-IV: Agrosphere Institute

K. Sabelefld
Weierstrass Institute for Applied Analysis and Stochastics, Berlin
Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of Russian Academy of Sciences

P. Knabner
Friedrich-Alexander University of Erlangen-Nuremberg, Institute of Applied Mathematics, Germany

Keywords

Ito equation; random fields; memory effects; ergodicity.

References

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Paper coordinates

N. Suciu, C. Vamoş, H. Vereecken, K. Sabelfeld P. Knabner, Itô equation model for dispersion of solutes in heterogeneous media, Rev. Anal. Numér. Théor. Approx., 37 (2008) no. 2, 221-238

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Journal

Rev. Anal. Numér. Théor. Approx.

Publisher Name

Editions de l’Academie Roumaine

Print ISSN

1222-9024

Online ISSN

2457-8126

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