Stochastic meshfree projection scheme for flow in random porous media

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Description/Abstract

We present a stochastic meshfree projection scheme for analysis of flow in random porous media. The random field describing the log-permeability is discretized using the Karhunen-Loeve expansion scheme. We perform spatial discretization of the governing equations by representing the pressure distribution using an expansion in terms of radial basis functions iwth undetermined random coefficents. Subsequently, we apply a collocation scheme over physical space, which leads to a system of linear random algebraic equations. The algetbraic equations are solved by Galerkin projection on to a preconditioned stochastic Krylove subspace. This enables the possibility of accurately estimating the statistics of the pressure distribution at a computational cost only marginally higher than the solution of the deterministic version of the governing equations. We present numerical results for two test cases to illustrate the performance of the proposed approach.