Dgfem for the Numerical Solution of Compressible Flow in Time Dependent Domains and Applications to Fluid-structure Interaction

Abstract. The paper is concerned with the simulation of inviscid and 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 Euler and Navier-Stokes equations describing compressible flow. They are discretized by the discontinuous Galerkin finite element method using piecewise polynomial discontinuous approximations. The time discretization is based on a semi-implicit linearized scheme, which leads to the solution of a linear algebraic system on each time level. Moreover, we use special treatment of boundary conditions and shock capturing, allowing the solution of flow with a wide range of Mach numbers. As a result we get an efficient and robust numerical process. The applicability of the developed method will be demonstrated by computational results obtained for compressible inviscid and viscous flow in channels with moving walls and flow induced airfoil vibrations.