In this article we present a one-field monolithic finite element method in the Arbitrary Lagrangian-Eulerian (ALE) formulation for Fluid-Structure Interaction (FSI) problems. The method only solves for one velocity field in the whole FSI domain, and it solves in a monolithic manner so that the fluid solid interface conditions are satisfied automatically. We prove that the proposed scheme is unconditionally stable, through energy analysis, by utilising a conservative formulation and an exact quadrature rule. We implement the algorithm using both ${\bf F}$-scheme and ${\bf d}$-scheme, and demonstrate that the former has the same formulation in two and three dimensions. Finally several numerical examples are presented to validate this methodology, including combination with remesh techniques to handle the case of very large solid displacement.

中文翻译：

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一种用于流固耦合的能量稳定单场整体任意拉格朗日-欧拉公式

在本文中，我们提出了一种用于流固耦合 (FSI) 问题的任意拉格朗日-欧拉 (ALE) 公式中的单场整体有限元方法。该方法只求解整个FSI域中的一个速度场，采用整体式求解，自动满足流固界面条件。我们通过能量分析，利用保守公式和精确求积规则证明了所提出的方案是无条件稳定的。我们同时使用 ${\bf F}$-scheme 和 ${\bf d}$-scheme 来实现算法，并证明前者在二维和三维上具有相同的公式。最后给出了几个数值例子来验证这种方法，包括结合网格技术来处理非常大的固体位移的情况。