论文标题
用于保留局部质量保护的Stokes-darcy问题的参数迭代方法
A Parameter-Robust Iterative Method for Stokes-Darcy Problems Retaining Local Mass Conservation
论文作者
论文摘要
我们分别考虑了由固定的stokes和darcy流动的自由流和多孔介质流的耦合模型。两个系统之间的耦合是通过引入代表界面上正常通量的单个变量来实现的。该问题仅减少到仅有关接口通量变量的系统，该系统在适当的加权规范中被证明是范围很好的。然后提出了一种迭代溶液方案来解决减少的问题，以便在每次迭代中保留质量。通过基于分析的加权规范引入预处理，迭代方案的性能在材料和离散参数方面是可靠的。根据构造，该方案适用于广泛的本地保守离散方案，我们考虑混合有限元方法框架中的明确示例。最后，使用数值实验证实了理论结果。
We consider a coupled model of free-flow and porous medium flow, governed by stationary Stokes and Darcy flow, respectively. The coupling between the two systems is enforced by introducing a single variable representing the normal flux across the interface. The problem is reduced to a system concerning only the interface flux variable, which is shown to be well-posed in appropriately weighted norms. An iterative solution scheme is then proposed to solve the reduced problem such that mass is conserved at each iteration. By introducing a preconditioner based on the weighted norms from the analysis, the performance of the iterative scheme is shown to be robust with respect to material and discretization parameters. By construction, the scheme is applicable to a wide range of locally conservative discretization schemes and we consider explicit examples in the framework of Mixed Finite Element methods. Finally, the theoretical results are confirmed with the use of numerical experiments.
