Versatile Two-Level Schwarz Preconditioners for Multiphase Flow

Abstract

Numerically modeling groundwater flow on finely discretized two- and three-dimensional domains requires solution algorithms appropriate for distributed memory multiprocessor architectures. Multilevel and domain decomposition algorithms are appropriate for preconditioning or solving linear systems in parallel and have, therefore, been applied to linear models for saturated groundwater flow. These algorithms have also been incorporated into more complex nonlinear multiphase flow models in the context of a linearization procedure such as Newton's method. In this work, we study a class of parallel preconditioners based on two-level Schwarz domain decomposition applied in a nonlinear two-phase flow numerical model. The restriction and interpolation operators are based on an aggregation approach that has a straightforward implementation for a variety of applications arising in subsurface modeling: structured and unstructured discretizations, finite elements and finite differences, and multicomponent model equations. We present model formulations, results from numerical experiments, and a comparison of a standard one-level Schwarz method to three two-level aggregation-based methods.