Iterative Methods with Nonconforming Time Grids for Nonlinear Flow Problems in Porous Media
Iterative Methods with Nonconforming Time Grids for Nonlinear Flow Problems in Porous Media
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DOI：
10.1007/s40306-022-00486-x
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发表时间：
2022-12
影响因子：
0.5
通讯作者：
Thi-Thao-Phuong Hoang;I. Pop
中科院分区：
文献类型：
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作者：
Thi-Thao-Phuong Hoang;I. Pop
多孔介质中的部分饱和流动通常通过理查兹方程进行建模，该方程是非线性的、抛物线的并且可能是退化的。本文提出了基于域分解的理查兹方程数值方案，其中不同的时间步可以用于不同的子域。以混合公式推导了两种全局时域分解方法：第一种方法基于物理传输条件，第二种方法基于等效 Robin 传输条件。对于每种方法，我们使用子结构技术将原始问题重写为在子域之间的时空界面上定义的非线性问题。这种时空界面问题使用牛顿法线性化，然后通过GMRES迭代求解；每次 GMRES 迭代都涉及子域中与时间相关的问题的并行求解。通过二维数值实验验证并比较了所提出的局部时间步进方法的收敛性和准确性。
Partially saturated flow in a porous medium is typically modeled by the Richards equation, which is nonlinear, parabolic and possibly degenerated. This paper presents domain decomposition-based numerical schemes for the Richards equation, in which different time steps can be used in different subdomains. Two global-in-time domain decomposition methods are derived in mixed formulations: the first method is based on the physical transmission conditions and the second method is based on equivalent Robin transmission conditions. For each method, we use substructuring techniques to rewrite the original problem as a nonlinear problem defined on the space-time interfaces between the subdomains. Such a space-time interface problem is linearized using Newton’s method and then solved iteratively by GMRES; each GMRES iteration involves parallel solution of time-dependent problems in the subdomains. Numerical experiments in two dimensions are carried out to verify and compare the convergence and accuracy of the proposed methods with local time stepping.