Simulation of compressible viscous flow in time-dependent domains

The paper is concerned with the simulation of viscous compressible flow in time dependent domains. The dependence on time of the domain occupied by the fluid is taken into account with the aid of the Arbitrary Lagrangian–Eulerian (ALE) formulation of the compressible Navier–Stokes equations. 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. A suitable treatment of boundary conditions and shock capturing are used, allowing the solution of flow with a wide range of Mach numbers. The applicability of the developed method is demonstrated by computational results obtained for compressible viscous flow in a channel with moving walls and flow induced airfoil vibrations.