Validation of a Computational Aeroacoustics Code for Nonlinear Flow about Complex Geometries Using Ringleb's Flow

This work is concerned with the validation of a high-accuracy Computational Aeroacoustics (CAA) code designed for use in the prediction of unsteady compressible flows about complex geometries, using Ringleb's analytic solution of the compressible steady Euler equations. The flow itself is nonlinear, in some cases transitioning from subsonic to supersoni c and back to subsonic without a shock. Using such an analytic solution of the compressible Euler equations results in a strong validation case for testing the wall boundary conditions used in the code. In such codes, the effect of the boundary conditions on the local flow can be instantaneously propagated many mesh points into the computational domain, affecting the evolution of the flow solution away from the boundary. With such a large stencil footprint, the treatment of the boundary condition has a large effect on code stability and accuracy. A matrix of test cases was run to investigate the effect for different wall geometries, which were defined by the streamlines of the analytical solution. In all the cases Tam and Webb’s optimized explicit fourth-order Dispersion-Relation-Preserving (DRP) central differencing scheme was used. The CAA code gave accurate results for complex geometries when this scheme was used. When the explicit second-order central differencing scheme was used non-physical shocks we re observed for the case involving transonic flow.