A Numerical Validation of a High-Order Finite-Difference Compact Scheme for Computational Aeroacoustics

Abstract

Computing sound directly from unsteady flows featuring large-scale instabilities requires numerical methods that can resolve the small amplitude perturbations of sound embedded in the large-amplitude hydrodynamic flow unsteadiness. The perturbations due to sound need to be propagated with an acceptable dispersion and dissipation over significant distances to adequately resolve in space the noise near field. In this paper, a high-order compact scheme is detailed that promise to deliver the small dispersion and dissipation characteristics to directly model the noise and the unsteadiness in low Mach number flows. The performance of the scheme is assessed by cross-comparison against selected benchmark problems from the first workshop on benchmark problems in Computational Aeroacoustics (CAA) and additional test cases, including the reflection of an acoustic pulse into a corner, which is a challenging application due to the confluence of two wall conditions at the corner. Analytical solutions for the test cases are also produced to validate the predictions. The numerical results show that the scheme achieves comparable performances in computing these relatively simple two-dimensional test problems, with levels of dispersion and dissipation comparable to that in the published literature from similar computational aeroacoustic schemes. The results give confidence in developing these scheme to tackle more complex, three-dimensional noise producing flows, of interest for practical engineering applications.