Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media

Journal Article · Thu Oct 26 00:00:00 EDT 2017 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/16M1082652· OSTI ID:1505960

Bui, Quan ^[1]; Elman, Howard ^[2]; Moulton, John David  ^[3]

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1. University of Maryland; Univ. of Maryland, College Park, MD (United States). Applied Math, Stats, and Scientic Computation
2. Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science
3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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. Finally, 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 both is efficient and scales optimally with problem size.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Office of Environmental Management (EM); National Science Foundation (NSF)
• Grant/Contract Number: 89233218CNA000001; SC0009301; DMS1418754; AC52-06NA25396
• OSTI ID: 1505960
• Report Number(s): LA-UR-16-28063
• Journal Information: SIAM Journal on Scientific Computing, Vol. 39, Issue 5; ISSN 1064-8275
• Publisher: SIAM
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Mathematics
Multiphase flow
preconditioning
multigrid