WIAS Preprint No. 786, (2002)

A Lagrangian stochastic model for the transport in statistically homogeneous porous media


  • Kurbanmuradov, Orazgeldy
  • Sabelfeld, Karl
  • Smidts, Olivier F.
  • Vereecken, Henry

2010 Mathematics Subject Classification

  • 65C05 76S05

2008 Physics and Astronomy Classification Scheme

  • 47.55.Mh


  • Porous media, Lognormal hydraulic conductivity, Stochastic and turbulent flows, stochastic Eulerian and Lagrangian models


A new type of stochastic simulation models is developed for solving transport problems in saturated porous media which is based on a generalized Langevin stochastic differential equation. A detailed derivation of the model is presented in the case when the hydraulic conductivity is assumed to be a random field with a lognormal distribution, being statistically isotropic in space. To construct a model consistent with this statistical information, we use the well-mixed condition which relates the structure of the Langevin equation and the probability density function of the Eulerian velocity field. Numerical simulations of various statistical characteristics like the mean displacement, the displacement covariance tensor and the Lagrangian correlation function are presented. These results are compared against the conventional random displacement method.

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