Stochastic polynomial chaos expansion method for random Darcy equation

Abstract

AbstractA probabilistic collocation based polynomial chaos expansion method is developed for simulation of particle transport in porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure. The flow is modeled in a two-dimensional domain with mixed Dirichlet–Neumann boundary conditions. The relevant Karhunen–Loève expansion is constructed by a special randomized singular value decomposition (SVD) of the correlation matrix which makes possible to treat problems of high dimension. The simulation results are compared against a direct Monte Carlo calculation of different Eulerian and Lagrangian statistical characteristics of the solutions. As a byproduct, we suggest an approach to solve an inverse problem of recovering the variance of the log-conductivity.