Fluid-structure interaction with $H(\text{div})$-conforming finite elements

Abstract

In this paper a novel application of the (high-order) $H(\text{div})$-conforming Hybrid Discontinuous Galerkin finite element method for monolithic fluid-structure interaction (FSI) is presented. The Arbitrary Lagrangian Eulerian (ALE) description is derived for $H(\text{div})$-conforming finite elements including the Piola transformation, yielding exact divergence free fluid velocity solutions. The arising method is demonstrated by means of the benchmark problems proposed by Turek and Hron [50]. With hp-refinement strategies singularities and boundary layers are overcome leading to optimal spatial convergence rates.

References in corpus (1)

• High-order arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the incompressible Navier-Stokes equations

Cited by in corpus (4)

• High-order arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the incompressible Navier-Stokes equations
• A conforming sliding mesh technique for an embedded-hybridized discontinuous Galerkin discretization for fluid-rigid body interaction
• An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows
• Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for fluid-structure interaction