Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids
KAUST DepartmentExtreme Computing Research Center
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Office of the President
Online Publication Date2020-02-07
Print Publication Date2020-05
Embargo End Date2022-02-07
Permanent link to this recordhttp://hdl.handle.net/10754/661699
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AbstractSimulation of subsurface flows in porous media is difficult due to the nonlinearity of the operators and the high heterogeneity of material coefficients. In this paper, we present a scalable fully implicit solver for incompressible two-phase flows based on overlapping domain decomposition methods. Specifically, an inexact Newton-Krylov algorithm with analytic Jacobian is used to solve the nonlinear systems arising from the discontinuous Galerkin discretization of the governing equations on 3D unstructured grids. The linear Jacobian system is preconditioned by additive Schwarz algorithms, which are naturally suitable for parallel computing. We propose a hybrid two-level version of the additive Schwarz preconditioner consisting of a nested coarse space to improve the robustness and scalability of the classical one-level version. On the coarse level, a smaller linear system arising from the same discretization of the problem on a coarse grid is solved by using GMRES with a one-level preconditioner until a relative tolerance is reached. Numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed solver for 3D heterogeneous medium problems. We also report the parallel scalability of the proposed algorithms on a supercomputer with up to 8,192 processor cores.
CitationLuo, L., Liu, L., Cai, X.-C., & Keyes, D. E. (2020). Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids. Journal of Computational Physics, 409, 109312. doi:10.1016/j.jcp.2020.109312
SponsorsThe first author was supported in part by the National Natural Science Foundation of China (11701547), the second author was supported in part by the National Natural Science Foundation of China (11901296) and by the Natural Science Foundation for Young Scientists of Jiangsu (BK20180450). This research was also supported by the Extreme Computing Research Center of the King Abdullah University of Science and Technology.
JournalJournal of Computational Physics