Itô equation model for dispersion of solutes in heterogeneous media
Keywords:
Itō equation, random fields, memory effects, ergodicityAbstract
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.Downloads
Download data is not yet available.
Downloads
Published
2008-08-01
How to Cite
Suciu, N., Vamoş, C., Vereecken, H., Sabelfeld, K., & Knabner, P. (2008). Itô equation model for dispersion of solutes in heterogeneous media. Rev. Anal. Numér. Théor. Approx., 37(2), 221–238. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2008-vol37-no2-art15
Issue
Section
Articles
License
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.