Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media
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 timeimplicit treatment of models of multiphase flow. We explore the performance of several preconditioners based on algebraic multigrid (AMG) for solving the linearized problem, including “blackbox” AMG applied directly to the system, a new version of constrained pressure residual multigrid (CPRAMG) 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.
 Authors:

 University of Maryland; Univ. of Maryland, College Park, MD (United States). Applied Math, Stats, and Scientic Computation
 Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Environmental Management (EM); National Science Foundation (NSF)
 OSTI Identifier:
 1505960
 Report Number(s):
 LAUR1628063
Journal ID: ISSN 10648275
 Grant/Contract Number:
 89233218CNA000001; SC0009301; DMS1418754; AC5206NA25396
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 39; Journal Issue: 5; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Mathematics; Multiphase flow; preconditioning; multigrid
Citation Formats
Bui, Quan, Elman, Howard, and Moulton, John David. Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media. United States: N. p., 2017.
Web. doi:10.1137/16M1082652.
Bui, Quan, Elman, Howard, & Moulton, John David. Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media. United States. doi:10.1137/16M1082652.
Bui, Quan, Elman, Howard, and Moulton, John David. Thu .
"Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media". United States. doi:10.1137/16M1082652. https://www.osti.gov/servlets/purl/1505960.
@article{osti_1505960,
title = {Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media},
author = {Bui, Quan and Elman, Howard and Moulton, John David},
abstractNote = {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 timeimplicit treatment of models of multiphase flow. We explore the performance of several preconditioners based on algebraic multigrid (AMG) for solving the linearized problem, including “blackbox” AMG applied directly to the system, a new version of constrained pressure residual multigrid (CPRAMG) 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.},
doi = {10.1137/16M1082652},
journal = {SIAM Journal on Scientific Computing},
issn = {10648275},
number = 5,
volume = 39,
place = {United States},
year = {2017},
month = {10}
}
Web of Science