WIAS Preprint No. 912, (2004)

Stochastic Eulerian model for the flow simulation in porous media. Unconfined aquifers


  • Kolyukhin, Dmitry R.
  • Sabelfeld, Karl

2010 Mathematics Subject Classification

  • 65C05 76N20


  • Hydraulic conductivity, Lognormal random field, small fluctuations, Darcy law, randomized spectral representation


This work deals with a stochastic unconfined aquifer flow simulation in statistically isotropic saturated porous media. This approach is a generalization of the 3D model we developed in citeks. In this paper we deal with a 2D model obtained via depth-averaging of the 3D model. The average hydraulic conductivity is assumed to be a random field with a lognormal distribution. Assuming the fluctuations in the hydraulic conductivity to be small we construct a stochastic Eulerian model for the flow as a Gaussian random field with a spectral tensor of a special structure derived from Darcy's law. A randomized spectral representation is then used to simulate this random field. A series of test calculations confirmed the high accuracy and computational efficiency of the method.

Appeared in

  • Monte Carlo Methods Appl. vol 10 (2004), no. 3-4, pp. 345-357

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