Abstract A scheme for the solution of fluid–structure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid equations, while the standard continuous Galerkin (CG) approach is adopted for the structural problem. The chosen HDG solver combines robustness of discontinuous Galerkin (DG) approaches in advection-dominated flows with higher-order accuracy and efficient implementations. Two coupling strategies are examined in this contribution, namely a partitioned Dirichlet–Neumann scheme in the context of hybrid HDG–CG discretizations and a monolithic approach based on Nitsche’s method, exploiting the definition of the numerical flux and the trace of the solution to impose the coupling conditions. Numerical experiments show optimal convergence of the HDG and CG primal and mixed variables and superconvergence of the postprocessed fluid velocity. The robustness and the efficiency of the proposed weakly compressible formulation, in comparison to a fully incompressible one, are also highlighted on a selection of two and three dimensional FSI benchmark problems.

中文翻译：

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一种用于流固耦合问题的弱可混合可混合不连续伽辽金公式

摘要 本文提出了一种求解弱可压缩流动的流固耦合 (FSI) 问题的方案。针对流体方程的离散化，推导出了一种新的可混合不连续伽辽金 (HDG) 方法，而对结构问题则采用了标准的连续伽辽金 (CG) 方法。所选择的 HDG 求解器将非连续伽辽金 (DG) 方法在对流主导流中的稳健性与高阶精度和高效实现相结合。在这个贡献中检查了两种耦合策略，即混合 HDG-CG 离散化背景下的分区 Dirichlet-Neumann 方案和基于 Nitsche 方法的整体方法，利用数值通量的定义和解的轨迹来强加耦合条件。数值实验表明 HDG 和 CG 原始和混合变量的最佳收敛以及后处理流体速度的超收敛。与完全不可压缩的公式相比，所提出的弱可压缩公式的鲁棒性和效率在选择的二维和三维 FSI 基准问题上也得到了强调。