The Interaction of Compressible Flow and an Elastic Structure Using Discontinuous Galerkin Method

In this paper we are concerned with the numerical simulation of the interaction of fluid flow and an elastic structure in a 2D domain. For each individual problem we employ the discretization by the discontinuous Galerkin finite element method (DGM). We describe the application of the DGM to the problem of compressible fluid flow in a time-dependent domain and also to the dynamic problem of the deformation of an elastic body. Finally, we present our approach to the coupling of these two independent problems: both are solved separately at a given time instant, but we require the approximate solutions to satisfy certain transient conditions. These transient conditions are met through several inner iterations. In each iteration a calculation of both the elastic body deformation problem and the problem of the compressible fluid flow is performed. The presented method can be applied to solve a selection of problems of biomechanics and aviation. Our numerical experiments are inspired by the simulation of airflow in human vocal folds, which implies the choice of the properties of the flowing fluid and the material properties of the elastic body. The results are post-processed in order to get a visualization of the approximate solution. We are especially interested in the visualization of the elastic body deformation and the visualization of some chosen physical quantities of the flow.