WIAS Preprint No. 1007, (2005)

Stochastic flow simulation in 3D porous media


  • Kolyukhin, Dmitry R.
  • Sabelfeld, Karl

2010 Mathematics Subject Classification

  • 65C05 76N20


  • Stochastic hydraulic conductivity, Lognormal random field, Darcy law, Randomized spectral representation, Lagrangian statistics, Mean squared separation




Stochastic models and Monte Carlo algorithms for simulation of flow through porous media beyond the small hydraulic conductivity fluctuation assumptions are developed. The hydraulic conductivity is modelled as an isotropic random field with a lognormal distribution and prescribed correlation or spectral functions. It is sampled by a Monte Carlo method based on a randomized spectral representation. The Darcy and continuity equations with the random hydraulic conductivity are solved numerically, using the successive over relaxation method in order to extract statistical characteristics of the flow. Hybrid averaging is used: we combine spatial and ensemble avergaing to get efficient numerical procedure. We provide some conceptual and numerical comparison of various stochastic simulation techniques, and focus on the prediction of applicability of the randomized spectral models derived under the assumption of small hydraulic conductivity fluctuations.

Appeared in

  • Monte Carlo Methods Appl., 11 (2005) pp. 15--37.

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