In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A five-field mixed-primal finite element scheme is proposed solving for Stokes velocity-pressure and Biot displacement-total pressure-fluid pressure. Adequate inf-sup conditions are derived, and one of the distinctive features of the formulation is that its stability is established robustly in all material parameters. We propose robust preconditioners for this perturbed saddle-point problem using appropriately weighted operators in fractional Sobolev and metric spaces at the interface. The performance is corroborated by several test cases, including the application to interfacial flow in the brain.

在本文中，我们推进了粘性牛顿流体的自由流动与由界面分离的可变形多孔介质之间的整体耦合的流固耦合模型的离散化分析。提出了一种求解Stokes速度-压力和Biot位移-总压力-流体压力的五场混合原始有限元格式。导出了足够的 inf-sup 条件，并且该配方的显着特征之一是其稳定性在所有材料参数中都得到了稳健的建立。我们在分数 Sobolev 和接口处的度量空间中使用适当加权的算子为这个受扰动的鞍点问题提出了鲁棒的预处理器。该性能得到了几个测试案例的证实，包括对大脑界面流动的应用。