Itô equation model for dispersion of solutes in heterogeneous media


  • N. Suciu Friedrich-Alexander University of Erlangen-Nuremberg
  • C. Vamoş Tiberiu Popoviciu Institute of Numerical Analysis
  • H. Vereecken Research Center Jülich
  • K. Sabelfeld Weierstrass Institute for Applied Analysis and Stochastics, Berlin
  • P. Knabner Friedrich-Alexander University of Erlangen-Nuremberg


Itō equation, random fields, memory effects, ergodicity


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.




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