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

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 \cite{ks}. 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