This work is concerned with the numerical solution of inviscid compressible fluid flow in moving domains. Specifically, we assume that the boundary part of the domain (impermeable walls) are time dependent. We consider the Euler equations, which describe the movement of inviscid compressible fluids. We present two formulations of the Euler equations in the ALE (Arbitrary Lagrangian-Eulerian) form. These two formulations are
discretized in space by the discontinuous Galerkin method. We apply a semi-implicit
linearization with respect to time to obtain a numerical scheme requiring the solution of only one linear system on each time level. We apply the method to the compressible flow around a moving (vibrating) profile.