High Order Difference Approximations for the Linearized Euler Equations

The computers of today make it possible to do direct simulation of aeroacoustics, which is very computationally demanding since a very high resolution is needed. In the present thesis we study issues of relevance for aeroacoustic simulations. Paper A considers standard high order difference methods. We study two different ways of applying boundary conditions in a stable way. Numerical experiments are done for the 1D linearized Euler equations. In paper B we develop strictly stable difference methods which give smaller dispersion errors than standard central difference methods. The new methods are applied to the 1D wave equation. Finally in Paper C we apply the new difference methods to aeroacoustic simulations based on the 2D linearized Euler equations. Taken together, the methods presented here are strictly stable by construction. They lead to better approximation of the wave number, which in turn results in a smaller L2-error than obtained by previous methods found in the literature. The results are valid when the problem is not fully resolved, which usually is the case for large scale applications.