Stochastic Krylov subspace methods for flow in random porous media

Abstract

AbstractThe present work establishes a comparative analysis of two different Krylov‐based methods for assessing uncertainty in porous media flow applications. They are: (1) the stochastic reduced basis method (SRBM) and the (2) Krylov‐Karhunen‐Loeve moment equation (KKLME). The former relies on the construction of an orthogonal basis from which projectors may be realized to perform the uncertainty analysis on a lower‐dimensional space. The second approach relies on the idea of expressing input and corresponding outputs in terms of stochastic and perturbative polynomial expansions. By grouping terms and moments of the same order, the original stochastic equation is replaced by successive (and parallel) solutions of a set of deterministic equations. We provide a set of numerical experiments illustrating the capabilities of SRBM and KKLME against Monte Carlo simulations (MCS) on stationary permeability cases. We show that KKLME is superior to SRBM. Furthermore, KKLME appears to be also a more efficient alternative than MCS for non‐stationary permeability field distributions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)