论文标题
能量稳定的一场单场单位任意的拉格朗日 - 欧拉 - 欧拉植物配方用于流体结构相互作用
An energy stable one-field monolithic arbitrary Lagrangian-Eulerian formulation for fluid-structure interaction
论文作者
论文摘要
在本文中，我们介绍了用于流体结构相互作用（FSI）问题的任意拉格朗日 - 欧拉（ALE）公式中的一场单片有限元方法。该方法仅在整个FSI结构域中求解一个速度场，并且以单片方式求解，以便自动满足流体固体界面条件。我们通过使用保守的公式和确切的正交规则来证明所提出的方案是通过能量分析无条件稳定的。我们使用$ {\ bf f} $ - 方案和$ {\ bf d} $ - 方案实现算法，并证明前者在两个和三个维度中具有相同的公式。最后，提出了几个数值示例来验证这种方法，包括与Remesh技术的组合来处理非常大的实心位移情况。
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.
