Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids
Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids
复制标题
3D非结构化网格上多孔介质两相流的完全隐式混合二级域分解算法
DOI：
10.1016/j.jcp.2020.109312
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发表时间：
2020-05
影响因子：
4.1
通讯作者：
David E. Keyes
中科院分区：
文献类型：
--
作者：
Li Luo;Lulu Liu;Xiao-Chuan Cai;David E. Keyes
由于算符的非线性和材料系数的高度非均质性，模拟多孔介质中的地下流动非常困难。本文提出了一种基于重叠区域分解方法的可伸缩全隐式不可压缩两相流求解器。具体地说，采用带解析雅可比矩阵的非精确Newton-Krylov算法求解三维非结构网格上由控制方程的不连续Galerkin离散引起的非线性系统。线性雅可比系统采用加性Schwarz算法进行预处理，自然适合于并行计算。我们提出了一种由嵌套粗糙空间组成的混合两层版本的加性Schwarz预条件，以提高经典一层版本的鲁棒性和可扩展性。在粗网格上，使用带一级预调节器的GMRES求解由粗网格上问题的相同离散化产生的较小的线性系统，直到达到相对容差。通过数值实验验证了该算法对三维非均质介质问题的有效性和高效性。我们还报告了所提出的算法在具有多达8,192个处理器核的超级计算机上的并行可扩展性。
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.
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DOI：
--
发表时间：
1995
期刊：
--
影响因子：
--
作者：
G. Karypis;Vipin Kumar
通讯作者：
G. Karypis;Vipin Kumar
DOI：
10.1137/120898358
发表时间：
2013-12
期刊：
SIAM J. Numer. Anal.
影响因子：
--
作者：
Jisheng Kou;Shuyu Sun
通讯作者：
Jisheng Kou;Shuyu Sun
DOI：
10.2118/12267-ms
发表时间：
1983
期刊：
--
影响因子：
--
作者：
R. Ewing;R. F. Heinemann
通讯作者：
R. Ewing;R. F. Heinemann
影响因子：
2.5
作者：
P. Bastian
通讯作者：
P. Bastian
影响因子：
2.7
作者：
Zhangxin Chen;R. Ewing
通讯作者：
Zhangxin Chen;R. Ewing