Dgfem for Interaction of Fluids and Nonlinear Elasticity

This paper is concerned with the numerical simulation of the interaction of compressible viscous flow with elastic structures. The flow is described by the compressible Navier-Stokes equations written in the arbitrary Lagrangian-Eulerian (ALE) form. For the elastic deformation we use 2D linear elasticity and nonlinear St. Venant-Kirchhoff and neo-Hookean models. The discretization of both flow problem and elasticity problem is realized by the discontinuous Galerkin finite element method (DGFEM). The main attention is paid to testing the DGFEM applied to the solution of elasticity problems. Then we present an example of the fluid-structure interaction (FSI). The applicability of the developed technique is demonstrated by several numerical experiments.