Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media

TL;DR

This paper develops and compares algebraic multigrid preconditioners for efficiently solving the large linear systems arising from fully coupled, time-implicit multiphase flow models in porous media, demonstrating robustness and scalability.

Contribution

It introduces new AMG-based preconditioners, including a block factorization approach, that improve robustness and efficiency for multiphase flow simulations.

Findings

New preconditioners outperform existing methods in robustness.

Block factorization preconditioner scales optimally with problem size.

Methods effectively handle effects of capillary pressures.

Abstract

Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential equations derived by considering the mass conservation of each phase (e.g., oil, water), along with constitutive laws for the relationship of phase velocity to phase pressure. In this study, we develop and study efficient solution algorithms for solving the algebraic systems of equations derived from a fully coupled and time-implicit treatment of models of multiphase flow. We explore the performance of several preconditioners based on algebraic multigrid (AMG) for solving the linearized problem, including "black-box" AMG applied directly to the system, a new version of constrained pressure residual multigrid (CPR-AMG) preconditioning, and a new preconditioner derived using an approximate Schur complement arising from the block factorization of the Jacobian. We show that the new methods are the most robust with respect to problem character as determined by varying effects of capillary pressures, and we show that the block factorization preconditioner is both efficient and scales optimally with problem size.