Stochastic Eulerian model for the flow simulation in porous media

Sabelfeld Karl and Kolyukhin Dmitry
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Sabelfeld Karl: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D - 10117 Berlin, Germany. E-mail: sabelfeld@wias-berlin.de
Kolyukhin Dmitry: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D - 10117 Berlin, Germany. E-mail: sabelfeld@wias-berlin.de

Monte Carlo Methods and Applications, 2003, vol. 9, issue 3, 271-290

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.

Keywords: Hydraulic conductivity; Lognormal random field; small fluctuation; Darcy law; randomized spectral representation (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1515/156939603322729021

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