Applications of High-Order Optimized Upwind Schemes for Computational Aeroacoustics

High-order optimized upwind dispersion-relation-preserving finite difference schemes are used for solving multidimensional acoustic wave propagation problems. The accuracy and the robustness of the schemes are tested for acoustic problems with various geometry and boundary conditions. Excellent agreements between the numerical and the analytical solutions indicate that the high-order optimized upwind schemes minimize not only the dispersion error but also the dissipation error while retaining the numerical stability. The simulation results have also demonstrated that the optimized upwind schemes damp out the spurious short waves automatically without the need of filter or explicit dissipation terms. The overall effectiveness of the high-order optimized upwind schemes is verified. The good numerical result of the problem of acoustic scattering by a sphere suggests that the optimized upwind schemes may be used to solve acoustic problems involving a relatively complex geometry.