SIAM Journal on Scientific Computing, Volume 43, Issue 4, Page A2923-A2948, January 2021.
We consider a moving domain, fluid-porohyperelastic structure interaction problem in a dual-mixed formulation. The fluid is described using the Navier--Stokes equations, and the porohyperelastic structure is described using the Biot equations. To solve this problem numerically, we propose two novel, partitioned, loosely coupled methods based on the generalized Robin boundary conditions. In the first partitioned method, the Navier--Stokes problem is solved separately from the Biot problem. In the second proposed method, the problem is further split by separating the Biot problem into a mechanics subproblem and a Darcy subproblem. We derive the energy estimates for the proposed methods on a simplified, linear problem and show that the first partitioned method is unconditionally stable. The second partitioned method is shown to be energy-stable if the structure is viscoelastic and if certain conditions on the problem parameters and the time step are satisfied. The performance of both methods is investigated in the numerical examples.

中文翻译：

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流体-多孔超弹性结构相互作用的数值模拟

SIAM 科学计算杂志，第 43 卷，第 4 期，第 A2923-A2948 页，2021 年 1 月。
我们在双重混合公式中考虑移动域、流体-多孔超弹性结构相互作用问题。流体使用 Navier--Stokes 方程描述，多孔超弹性结构使用 Biot 方程描述。为了在数值上解决这个问题，我们提出了两种基于广义罗宾边界条件的新的、分区的、松耦合的方法。在第一种分区方法中，Navier-Stokes 问题与 Biot 问题分开解决。在提出的第二种方法中，通过将 Biot 问题分解为一个力学子问题和一个 Darcy 子问题来进一步拆分问题。我们在一个简化的线性问题上推导出所提出的方法的能量估计，并表明第一个分区方法是无条件稳定的。如果结构是粘弹性的，并且满足问题参数和时间步长的某些条件，则表明第二种分区方法是能量稳定的。在数值例子中研究了这两种方法的性能。