Discontinuous Galerkin Method for the Solution of Elasto-Dynamic and Fluid-Structure Interaction Problems

Abstract

This paper is concerned with the numerical solution of dynamic elasticity by the discontinuous Galerkin (dG) method. We consider the linear and nonlinear St. Venant-Kirchhoff model. The dynamic elasticity problem is split into two systems of first order in time. They are discretized by the discontinuous Galerkin method in space and backward difference formula in time. The developed method is tested by numerical experiments. Then the method is combined with the space-time dG method for the solution of compressible flow in a time dependent domain and used for the numerical simulation of fluid-structure interaction.