An Adaptive Preconditioner for Three-Dimensional Single-Phase Compressible Flow in Highly Heterogeneous Porous Media

Abstract

Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 155-177, March 2024.
Abstract. In this paper, we study two-grid preconditioners for three-dimensional single-phase nonlinear compressible flow in highly heterogeneous porous media arising from reservoir simulation. Our goal is to develop robust and efficient preconditioners that converge independently of the contrast of the media and types of boundary conditions and source term. This is accomplished by constructing coarse space that can capture important features of the local heterogeneous media. To detect these features, local eigenvalue problems are defined and eigenvectors are adaptively selected to form the coarse space. The coarse space just needs to be constructed only once with parallel computing, although the compressible flow is a time-dependent problem and the permeability field changes in different time steps. Smoothers such as Gauss–Seidel iteration and ILU(0) are used to remove high-frequency errors. We analyze this preconditioner by proving the smoothing property and approximation property. In particular, a new coarse interpolation operator is defined to facilitate the analysis. Extensive numerical experiments with different types of large-scale heterogeneous permeability fields and boundary conditions are provided to show the impressive performance of the proposed preconditioner.