Discontinuous Galerkin Method for the Solution of Fluid-Structure Interaction Problems with Applications to the Vocal Folds Vibration

Abstract

The goal of this paper is the numerical simulation of vocal folds vibration excited by compressible viscous flow. It is necessary to describe the flow by the compressible Navier-Stokes equations in a time-dependent domain, solved by the ALE method. The vibrations of the vocal folds are modelled by the nonlinear dynamic St. Venant-Kirchhoff elasticity theory. For the flow problem we employ the discretization by the space-time discontinuous Galerkin method (STDGM) and for the elasticity problem the backward difference formula in time and discontinuous Galerkin method in space (BDF-DGM). The flow and elasticity problems are strongly coupled. We show that it is more appropriate to use the nonlinear elasticity model in contrast to linear elasticity model.KeywordsCompressible flowTime-dependent domainALE methodDynamic elasticitySt. Venant-Kirchhoff modelVibrations of elastic structuresFluid-structure interactionSimulation of vocal fold vibration