Computation of the Aliasing and the Interface Transmission Benchmark Problems by the Dispersion-Relation-Preserving Scheme

The aliasing and the interface transmission benchmark problems are computed by the Dispersion-Relation-Preserving (DRP) scheme. The spatial resolution as well as possible wave propagation error of the DRP scheme can be quantified in wave number space. This allows the choice of a minimum size computation stencil that will provide accurate numerical solutions to these problems. The interface transmission problem involves a surface of discontinuity. Numerical treatment of boundary conditions at such a discontinuity is not well established in Computational Fluid Dynamics (CFD) and Computational Aeroacoustics (CAA). Here a ghost point method is introduced to impose the interface boundary conditions. Furthermore, the problem involves wave propagation in an infinitely large two-dimensional domain. Special consideration is required to perform the computation in a finite domain.