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

Kolyukhin Dmitry
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Kolyukhin Dmitry: Weierstrass Institute for Applied Analysis and Stochastics Mohrenstra”se 39, D - 10117 Berlin, Germany

Monte Carlo Methods and Applications, 2004, vol. 10, issue 3-4, 345-357

Abstract: 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 [13]. 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.

Date: 2004
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DOI: 10.1515/mcma.2004.10.3-4.345

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