Space-Time Domain Decomposition for Reduced Fracture Models in Mixed Formulation
Space-Time Domain Decomposition for Reduced Fracture Models in Mixed Formulation
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DOI：
10.1137/15m1009651
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发表时间：
2015-02
期刊：
影响因子：
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通讯作者：
T. Hoang;C. Japhet;M. Kern;J. Roberts
中科院分区：
文献类型：
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作者：
T. Hoang;C. Japhet;M. Kern;J. Roberts
在本文中，我们对“快速路径”裂缝感兴趣，我们的目标是使用全局时间、非重叠域分解方法来模拟包含此类裂缝的多孔介质中的流动和传输问题。我们考虑一个简化模型，其中裂缝被视为两个子域之间的界面。考虑两种域分解方法：一种使用时间相关的 SteklovPoincare 算子，另一种使用基于 Ventcell 传输条件的优化 Schwarz 波形弛豫 (OSWR)。对于每种方法，都推导了时空界面上界面问题的混合公式，并采用不同的时间网格来适应子域和裂缝中的不同时间尺度。针对混合公式给出了 Ventcell 子域问题的适定性证明。分析了存在裂缝情况下OSWR算法的收敛因子，计算出优化参数。给出了具有强异质性的二维问题的数值结果来说明这两种方法的性能。
In this paper we are interested in the "fast path" fracture and we aim to use global-in-time, nonoverlapping domain decomposition methods to model flow and transport problems in a porous medium containing such a fracture. We consider a reduced model in which the fracture is treated as an interface between the two subdomains. Two domain decomposition methods are considered: one uses the time-dependent SteklovPoincare operator and the other uses optimized Schwarz waveform relaxation (OSWR) based on Ventcell transmission conditions. For each method, a mixed formulation of an interface problem on the space-time interface is derived, and different time grids are employed to adapt to different time scales in the subdomains and in the fracture. Demonstrations of the well-posedness of the Ventcell subdomain problems is given for the mixed formulation. An analysis for the convergence factor of the OSWR algorithm is given in the case with fractures to compute the optimized parameters. Numerical results for two-dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods.