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Title: 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 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.

Authors:
 [1];  [2]; ORCiD logo [3]
  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)
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):
LA-UR-16-28063
Journal ID: ISSN 1064-8275
Grant/Contract Number:  
89233218CNA000001; SC0009301; DMS1418754; AC52-06NA25396
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 1064-8275
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 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.},
doi = {10.1137/16M1082652},
journal = {SIAM Journal on Scientific Computing},
issn = {1064-8275},
number = 5,
volume = 39,
place = {United States},
year = {2017},
month = {10}
}

Journal Article:
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