WIAS Preprint No. 836, (2003)

Stochastic Eulerian model for the flow simulation in porous media


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

2010 Mathematics Subject Classification

  • 65C05 76N20


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




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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