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Stochastic polynomial chaos expansion method for random Darcy equation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shalimova Irina A. & Sabelfeld Karl K., 2017. "Stochastic polynomial chaos expansion method for random Darcy equation," Monte Carlo Methods and Applications, De Gruyter, vol. 23(2), pages 101-110, June.
    • Handle: RePEc:bpj:mcmeap:v:23:y:2017:i:2:p:101-110:n:7
    DOI: 10.1515/mcma-2017-0109
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    References listed on IDEAS

    as
    1. Sabelfeld, K.K. & Mozartova, N.S., 2011. "Sparsified Randomization algorithms for low rank approximations and applications to integral equations and inhomogeneous random field simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 295-317.
    2. S. S. Isukapalli & A. Roy & P. G. Georgopoulos, 1998. "Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems," Risk Analysis, John Wiley & Sons, vol. 18(3), pages 351-363, June.
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