This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid–structure interaction problems. We model the fluid using incompressible Navier–Stokes equations, and the structure using linear elasticity equations. We assume that the structure is thick, that is, described in the same dimension as the fluid. We propose a non-iterative, domain decomposition method where the fluid and the structure subproblems are solved separately. The method is based on generalized Robin boundary conditions, which are used in both fluid and structure subproblems. Using energy estimates, we show that the proposed method applied to a moving domain problem is unconditionally stable. We also analyze the convergence of the method and show convergence in time and optimal convergence in space. Numerical examples are used to demonstrate the performance of the method. In particular, we explore the relation between the combination parameter used in the derivation of the generalized Robin boundary conditions and the accuracy of the scheme. We also compare the performance of the method to a monolithic solver.

中文翻译：

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一种流体与厚结构相互作用的非迭代域分解方法

这项工作的重点是开发和分析用于移动域、流固耦合问题的分区数值方法。我们使用不可压缩的 Navier-Stokes 方程对流体进行建模，并使用线性弹性方程对结构进行建模。我们假设结构是厚​​的，即在与流体相同的维度上描述。我们提出了一种非迭代的域分解方法，其中流体和结构子问题是分开解决的。该方法基于广义 Robin 边界条件，可用于流体和结构子问题。使用能量估计，我们表明所提出的应用于移动域问题的方法是无条件稳定的。我们还分析了该方法的收敛性并显示时间收敛和空间最优收敛。数值例子用于证明该方法的性能。特别地，我们探索了用于推导广义罗宾边界条件的组合参数与方案精度之间的关系。我们还将该方法的性能与整体求解器进行了比较。