WIAS Preprint No. 836, (2003)

Stochastic Eulerian model for the flow simulation in porous media



Authors

  • Kolyukhin, Dmitry R.
  • Sabelfeld, Karl K.

2010 Mathematics Subject Classification

  • 65C05 76N20

Keywords

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

DOI

10.20347/WIAS.PREPRINT.836

Abstract

This work deals with the stochastic flow simulation in statistically isotropic and anisotropic saturated porous media in 3D case. The hydraulic conductivity is assumed to be a random field with lognormal distribution. Under the assumption of smallness of fluctuations in the hydraulic conductivity we construct a stochastic Eulerian model for the incompressible flow as a divergenceless 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. Numerical results are compared with the analytical results obtained by the small pertrubation expansion. A series of test calculations confirmed the high accuracy and computational efficiency of the method. Comparisons with asymptotically exact results show a good agreement.

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