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O. Kurbanmuradov, K. Sabelfeld, O.F. Smidts, H. Vereecken
A Lagrangian Stochastic Model for the Transport in Statistically Homogeneous Porous Media
Keywords: 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 Direct Simulation Method.
Monte Carlo Methods and Applications, Walter de Gruyter
Print ISSN: 0929-9629
Volume: 9, 12/2003
Pages: 341 - 366