Analysis of Long Time Stability and Errors of Two Partitioned Methods for Uncoupling Evolutionary Groundwater-Surface Water Flows
Analysis of Long Time Stability and Errors of Two Partitioned Methods for Uncoupling Evolutionary Groundwater-Surface Water Flows
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DOI：
10.1137/110834494
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发表时间：
2013-01
期刊：
影响因子：
--
通讯作者：
W. Layton;Hoang Tran;C. Trenchea
中科院分区：
文献类型：
--
作者：
W. Layton;Hoang Tran;C. Trenchea
对地下水和地表水的多物理耦合的最有效模拟必须涉及采用最佳地下水编码和最佳地表水编码。分块方法通过逐次解子物理问题来解决耦合问题，最近研究了在有界时间区间(常数以指数形式增长)上建立收敛的Stokes-Darcy耦合问题。本文分析和测试了求解完全演化的Stokes-Darcy问题的两种这样的分割方法(非迭代的，区域分解)。在适当的时间步长限制下，证明了这两种划分方法的无条件、长时间(大于$0)稳定性。由此我们得到了在时间上一致于$0的最优误差估计。
The most effective simulations of the multiphysics coupling of groundwater to surface water must involve employing the best groundwater codes and the best surface water codes. Partitioned methods, which solve the coupled problem by successively solving the subphysics problems, have recently been studied for the Stokes--Darcy coupling with convergence established over bounded time intervals (with constants growing exponentially in $t$). This report analyzes and tests two such partitioned (noniterative, domain decomposition) methods for the fully evolutionary Stokes--Darcy problem. Under a modest time step restriction of the form $\Delta t\leq C$, where $C=C$ (physical parameters), we prove unconditional, long time (over $0\leq t<\infty $) stability of both partitioned methods. From this we derive an optimal error estimate that is uniform in time over $0\leq t<\infty$.