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    Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids

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    Type
    Article
    Authors
    Luo, Li cc
    Liu, Lulu
    Cai, Xiao Chuan cc
    Keyes, David E. cc
    KAUST Department
    Extreme Computing Research Center
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Office of the President
    Date
    2020-02-07
    Online Publication Date
    2020-02-07
    Print Publication Date
    2020-05
    Embargo End Date
    2022-02-07
    Submitted Date
    2019-08-20
    Permanent link to this record
    http://hdl.handle.net/10754/661699
    
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    Abstract
    Simulation 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.
    Citation
    Luo, 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
    Sponsors
    The 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.
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2020.109312
    Additional Links
    https://linkinghub.elsevier.com/retrieve/pii/S0021999120300863
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2020.109312
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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