Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for fluid-structure interaction

TL;DR

This paper introduces a high-order hybridizable discontinuous Galerkin scheme for fluid-structure interaction problems, combining ALE framework, novel discretizations, and interface enforcement methods, demonstrating good performance on benchmark tests.

Contribution

The paper presents a novel high-order HDG scheme for FSI problems, integrating divergence-free discretization, ALE framework, and interface methods, advancing numerical accuracy and stability.

Findings

Good performance on classical benchmark problems

Effective interface condition enforcement

High-order accuracy demonstrated

Abstract

We present a novel (high-order) hybridizable discontinuous Galerkin (HDG) scheme for the fluid-structure interaction (FSI) problem. The (moving domain) incompressible Navier-Stokes equations are discretized using a divergence-free HDG scheme within the arbitrary Lagrangian-Euler (ALE) framework. The nonlinear elasticity equations are discretized using a novel HDG scheme with an H(curl)-conforming velocity/displacement approximation. We further use a combination of the Nitsche's method (for the tangential component) and the mortar method (for the normal component) to enforce the interface conditions on the fluid/structure interface. A second-order backward difference formula (BDF2) is use for the temporal discretization. Numerical results on the classical benchmark problem by Turek and Hron show a good performance of our proposed method.