This article is cited in 3 papers

Solution to a stochastic Darcy equation by the polynomial chaos expansion

I. A. Shalimova, K. K. Sabelfeld

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev av., Novosibirsk, 630090, Russia

Abstract: This paper deals with the solution of a boundary value problem for the Darcy equation with a random hydraulic conductivity field. We use an approach based on the polynomial chaos expansion in the probability space of input data. We use the probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. A computational complexity of this algorithm is defined by the order of a polynomial chaos expansion and the number of terms in the Karhunen–Loève expansion. We calculate different Eulerian and Lagrangian statistical characteristics of the flow by the Monte Carlo and probabilistic collocation methods. Our calculations show a significant advantage of the probabilistic collocation method in comparison with the conventional direct Monte Carlo algorithm.

Key words: polynomial chaos, probabilistic collocation method, Darcy equation, Monte Carlo method, Karhunen–Loève expansion.

UDC: 519.245+519.676+539.2

Received: 15.07.2016
Revised: 23.11.2016

DOI: 10.15372/SJNM20170307

 English version: Numerical Analysis and Applications, 2017, 10:3, 259–271

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