In this work, we present a new monolithic finite element strategy for solving fluid–structure interaction problems involving a compressible fluid and a hyperelastic structure. In the Lagrangian limit, the time-stepping strategy that we propose conserves the total energy, and linear and angular momenta. Detailed proofs with numerical validations are provided. We use a displacement-based Lagrangian formulation for the structure, and a velocity-based arbitrary Lagrangian–Eulerian mixed formulation with appropriately chosen interpolations for the various field variables to ensure stability of the resulting numerical procedure. A hybrid formulation is used to prevent locking of thin structures. Apart from physical variables such as displacement, velocity, and so forth, no new variables are introduced in the formulation. The use of the exact tangent stiffness matrix ensures that the algorithm converges quadratically within each time step. A number of benchmark examples have been solved to illustrate the good performance of the proposed method.

中文翻译：

---

用于涉及可压缩流体的流固耦合问题的整体任意拉格朗日-欧拉有限元策略

在这项工作中，我们提出了一种新的整体有限元策略，用于解决涉及可压缩流体和超弹性结构的流固耦合问题。在拉格朗日极限中，我们提出的时间步进策略保存了总能量以及线性和角动量。提供了带有数值验证的详细证明。We use a displacement-based Lagrangian formulation for the structure, and a velocity-based arbitrary Lagrangian–Eulerian mixed formulation with appropriately chosen interpolations for the various field variables to ensure stability of the resulting numerical procedure. 混合公式用于防止锁定薄结构。除了位移、速度等物理变量外，公式中没有引入新变量。使用精确切线刚度矩阵可确保算法在每个时间步长内二次收敛。已经解决了许多基准示例，以说明所提出方法的良好性能。