A weakly compressible hybridizable discontinuous Galerkin formulation for fluid-structure interaction problems

TL;DR

This paper introduces a novel hybridizable discontinuous Galerkin method for weakly compressible fluid-structure interaction problems, demonstrating improved accuracy, robustness, and efficiency over traditional approaches through numerical experiments.

Contribution

It develops a new HDG-based discretization scheme for weakly compressible flows in FSI problems, combining partitioned and monolithic coupling strategies with proven convergence and superconvergence properties.

Findings

Optimal convergence of variables achieved

Superconvergence of fluid velocity demonstrated

Enhanced robustness and efficiency over incompressible models

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.