A posteriori error estimates and adaptive mesh refinement for the Stokes-Brinkman problem
A posteriori error estimates and adaptive mesh refinement for the Stokes-Brinkman problem
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Stokes-Brinkman 问题的后验误差估计和自适应网格细化
DOI：
10.1016/j.matcom.2019.05.015
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
B. Sousedík
中科院分区：
文献类型：
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作者：
Kevin Williamson;P. Burda;B. Sousedík
Stokes-Brinkman方程通过将渗流的Stokes模型和Darcy模型组合成单一的方程组来模拟非均质多孔介质中的渗流。有了适当的参数，这些方程就可以在不详细了解两个区域之间的界面的情况下模拟两个流动中的任何一个。因此，Stokes-Brinkman方程提供了一种替代耦合Darcy-Stokes模型的方法。在简要回顾了Stokes-Brinkman问题及其Taylor-Hood有限元离散之后，我们提出了一种基于残差的后验误差估计，并将其用于驱动自适应网格加密过程。我们比较了几种网格加密策略，并通过二维和三维的数值实验验证了其有效性。
The Stokes–Brinkman equations model flow in heterogeneous porous media by combining the Stokes and Darcy models of flow into a single system of equations. With suitable parameters, the equations can model either flow without detailed knowledge of the interface between the two regions. Thus, the Stokes–Brinkman equations provide an alternative to coupled Darcy–Stokes models. After a brief review of the Stokes–Brinkman problem and its discretization using Taylor–Hood finite elements, we present a residual-based a posteriori error estimate and use it to drive an adaptive mesh refinement process. We compare several strategies for the mesh refinement, and demonstrate its effectiveness by numerical experiments in both 2D and 3D.