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A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media
Abstract
Simulation of multiphase poromechanics involves solving a multiphysics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also known as monolithic approaches, are usually preferred. The main bottleneck of a monolithic approach is that it requires solution of large linear systems that result from the discretization and linearization of the governing balance equations. Because such systems are nonsymmetric, indefinite, and highly illconditioned, preconditioning is critical for fast convergence. Recently, most efforts in designing efficient preconditioners for multiphase poromechanics have been dominated by physicsbased strategies. Current stateoftheart “blackbox” solvers such as algebraic multigrid (AMG) are ineffective because they cannot effectively capture the strong coupling between the mechanics and the flow subproblems, as well as the coupling inherent in the multiphase flow and transport process. In this work, we develop an algebraic framework based on multigrid reduction (MGR) that is suited for tightly coupled systems of PDEs. Using this framework, the decoupling between the equations is done algebraically through defining appropriate interpolation and restriction operators. One can then employ existing solvers for each of the decoupled blocks or design a new solver based on knowledge of the physics.more »
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1607853
 Report Number(s):
 LLNLJRNL772001
Journal ID: ISSN 10648275; 963573
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 42; Journal Issue: 2; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; multigrid reduction; algebraic multigrid; multiphase flow; poromechanics; porous media
Citation Formats
Bui, Quan M., OseiKuffuor, Daniel, Castelletto, Nicola, and White, Joshua A. A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media. United States: N. p., 2020.
Web. doi:10.1137/19M1256117.
Bui, Quan M., OseiKuffuor, Daniel, Castelletto, Nicola, & White, Joshua A. A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media. United States. doi:10.1137/19M1256117.
Bui, Quan M., OseiKuffuor, Daniel, Castelletto, Nicola, and White, Joshua A. Thu .
"A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media". United States. doi:10.1137/19M1256117.
@article{osti_1607853,
title = {A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media},
author = {Bui, Quan M. and OseiKuffuor, Daniel and Castelletto, Nicola and White, Joshua A.},
abstractNote = {Simulation of multiphase poromechanics involves solving a multiphysics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also known as monolithic approaches, are usually preferred. The main bottleneck of a monolithic approach is that it requires solution of large linear systems that result from the discretization and linearization of the governing balance equations. Because such systems are nonsymmetric, indefinite, and highly illconditioned, preconditioning is critical for fast convergence. Recently, most efforts in designing efficient preconditioners for multiphase poromechanics have been dominated by physicsbased strategies. Current stateoftheart “blackbox” solvers such as algebraic multigrid (AMG) are ineffective because they cannot effectively capture the strong coupling between the mechanics and the flow subproblems, as well as the coupling inherent in the multiphase flow and transport process. In this work, we develop an algebraic framework based on multigrid reduction (MGR) that is suited for tightly coupled systems of PDEs. Using this framework, the decoupling between the equations is done algebraically through defining appropriate interpolation and restriction operators. One can then employ existing solvers for each of the decoupled blocks or design a new solver based on knowledge of the physics. We demonstrate the applicability of our framework when used as a “blackbox” solver for multiphase poromechanics. Here, we show that the framework is flexible to accommodate a wide range of scenarios, as well as efficient and scalable for large problems.},
doi = {10.1137/19M1256117},
journal = {SIAM Journal on Scientific Computing},
number = 2,
volume = 42,
place = {United States},
year = {2020},
month = {3}
}