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Stochastic Eulerian model for the flow simulation in porous media

Author

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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)

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.

Suggested Citation

  • Sabelfeld Karl & Kolyukhin Dmitry, 2003. "Stochastic Eulerian model for the flow simulation in porous media," Monte Carlo Methods and Applications, De Gruyter, vol. 9(3), pages 271-290, September.
    • Handle: RePEc:bpj:mcmeap:v:9:y:2003:i:3:p:271-290:n:7
    DOI: 10.1515/156939603322729021
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    References listed on IDEAS

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    1. Kurbanmuradov O. & Sabelfeld K. & Koluhin D., 1997. "Stochastic Lagrangian Models for Two-Particle Motion in Turbulent Flows. Numerical Results," Monte Carlo Methods and Applications, De Gruyter, vol. 3(3), pages 199-224, December.
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    Cited by:

    1. Kolyukhin Dmitry & Sabelfeld Karl, 2005. "Stochastic flow simulation in 3D porous media," Monte Carlo Methods and Applications, De Gruyter, vol. 11(1), pages 15-37, March.

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