Stochastic polynomial chaos expansion method for random Darcy equation

Shalimova Irina A. () and Sabelfeld Karl K. ()
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Shalimova Irina A.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia
Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2017, vol. 23, issue 2, 101-110

Abstract: A 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.

Keywords: Polynomial chaos; probabilistic collocation; Karhunen–Loève expansion; Darcy equation; Monte Carlo direct simulation (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1515/mcma-2017-0109

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