Effects of boundary schemes on computations of acoustic waves generated by vortical flows near a wall

Abstract

In this paper, direct numerical simulations of the sound from vortex dipole rebound from an adiabatic non-slip wall are performed to investigate the impacts of the boundary schemes combined with the 6^th order compact scheme on the capability of capturing the acoustic waves generated by vortical flows near a wall. The free parameter of the compact filter α=0.45 and α=0.49 are chosen to clarify effects of boundary schemes in high wave number region. Results show that some boundary schemes make the computations unstable and high order boundary schemes are not always appropriate. It is found that in the case of α=0.45, no remarkable difference is found in the results computed by each boundary scheme. On the other hand, in the case of α=0.49, the vorticity of vortex dipole almost does not depend on the each scheme. However, the vorticity of secondary vortex on the wall computed depends on the each boundary scheme and spatial resolution. This causes large difference in the distributions of vorticity and sound waves. It is therefore clearly understood that the characteristics of the first derivative of the boundary schemes combined with the 6^th order compact scheme in the high wave number band affect the capability to precisely capture the aerodynamic sound. When the compact filter's free parameter is chosen to be α=0.49, the boundary schemes have a strong influence on the computation of aerodynamic sound. Special attention to a combination of boundary and compact schemes is required to perform accurate computations of aerodynamic sound generated by flows near a wall.