Adaptive Stroud Stochastic Collocation Method for Flow in Random Porous Media via Karhunen-Loève Expansio (Communications in Computational Physics, 2008)
In this paper we develop a Stochastic Collocation Method (SCM) for flowin randomly heterogeneous porous media. At first, the Karhunen-Loève expansion istaken to decompose the log transformed hydraulic conductivity field, which leads toa stochastic PDE that only depends on a finite number of i.i.d. Gaussian random variables. Based on the eigenvalue decay property and a rough error estimate of Stroudcubature in SCM, we propose to subdivide the leading dimensions in the integrationspace for random variables to increase the accuracy. We refer to this approach as adaptive Stroud SCM. One- and two-dimensional steady-state single phase flow examplesare simulated with the new method, and comparisons are made with other stochasticmethods, namely, the Monte Carlo method, the tensor product SCM, and the quasi-Monte Carlo SCM. The results indicate that the adaptive Stroud SCM is more efficientand the statistical moments of the hydraulic head can be more accurately estimated.