Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 422, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2020.109745
Keywords
Reservoir simulation; Fully implicit method; Multilevel method; Restricted Schwarz preconditioners; Parallel computing
Funding
- National Natural Science Foundation of China [11971006, 11871069]
- Outstanding Young Foundation of Hunan Province Natural Science [2020JJ2002]
- PetroChina Innovation Foundation [2019D-5007-0213]
- Beijing Natural Science Foundation [JQ18001]
- Beijing Academy of Artificial Intelligence
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Parallel algorithms and simulators with good scalabilities are particularly important for large-scale reservoir simulations on modern supercomputers with a large number of processors. In this paper, we introduce and study a family of highly scalable multilevel restricted additive Schwarz (RAS) methods for the fully implicit solution of subsurface flows with Peng-Robinson equation of state in two and three dimensions. With the use of a second-order fully implicit scheme, the proposed simulator is unconditionally stable with the relaxation of the time step size by the stability condition. The investigation then focuses on the development of several types of multilevel overlapping additive Schwarz methods for the preconditioning of the resultant linear system arising from the inexact Newton iteration, and some fast solver technologies are presented for the assurance of the multilevel approach efficiency and scalability. We numerically show that the proposed fully implicit framework is highly efficient for solving both standard benchmarks as well as realistic problems with several hundreds of millions of unknowns and scalable to 8192 processors on the Tianhe-2 supercomputer. (C) 2020 Elsevier Inc. All rights reserved.
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