Discontinuous Galerkin Method and Applications to Fluid-Structure Interaction Problems

摘要

The subject of the paper is the numerical simulation of viscous compressible flow in time dependent domains. The motion of the boundary of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the Navier-Stokes equations. The flow problem is coupled with the dynamical linear elasticity problem. Both problems are discretized in space by the discontinuous Galerkin (DG) finite element method using piecewise polynomial discontinuous approximations. The time discretization is carried out by the BDF scheme or the DG in time. The developed methods are tested by numerical experiments and applied to the solution of a fluid-structure interaction problem.