Partitioned Time Stepping Method for Fully Evolutionary Stokes-Darcy Flow with Beavers-Joseph Interface Conditions
Partitioned Time Stepping Method for Fully Evolutionary Stokes-Darcy Flow with Beavers-Joseph Interface Conditions
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DOI：
10.1137/110828095
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
Li Shan;Haibiao Zheng
中科院分区：
文献类型：
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作者：
Li Shan;Haibiao Zheng
在这份报告中，一个分区的时间步进算法的瞬态流在矩阵域耦合到一个自由流在嵌入管道进行了分析。耦合流动由完全演化的Stokes-Darcy问题模拟。这种方法只需要解决一个，非耦合的斯托克斯和达西子物理和子域每个时间步。在基体和导管之间的界面上，施加Beavers-Joseph界面条件，而不是简化的Beavers-Joseph-Saffman条件。在一个适度的时间步长限制的形式$\三角形t\leq C$，其中$C=C$（物理参数），我们证明了该方法的稳定性。我们还得到误差估计。数值试验验证了理论结果的有效性。
In this report, a partitioned time stepping algorithm for transient flow in a matrix domain coupled to a free flow in embedded conduits is analyzed. The coupled flow is modeled by the fully evolutionary Stokes--Darcy problem. This method requires solving only one, uncoupled Stokes and Darcy subphysics and subdomain per time step. On the interface between the matrix and conduit, Beavers--Joseph interface conditions, instead of the simplified Beavers--Joseph--Saffman condition, are imposed. Under a modest time step restriction of the form $\triangle t\leq C$, where $C=C$ (physical parameters) we prove stability of the method. We also derive error estimates. Numerical tests illustrate the validity of the theoretical results.