Modifications of WENO schemes and their applications on the shock-associated noise of the supersonic jet

The supersonic jet is a multi-scale complex flow problem that involves shock waves, vortices, turbulence, and sound waves.The shock-associated noise generated by the supersonic jet and its numerical method are key concerns of aeroacoustics.The weighted essentially non-oscillatory (WENO) scheme and its derived shockcapturing techniques are widely used in numerical simulations of the flow with shock waves.However, WENO schemes aim to eliminate or minimize nonphysical spurious waves around shocks, which often leads to the dissipation of sound waves.Therefore, it is imperative to modify WENO schemes to effectively capture both shock and sound waves.In this paper, we briefly review the strategies to improve the shock-associated noise computation ability of the WENO schemes, including the technique to reduce non-physical oscillation near the shock and a criterion to design the smoothness indicator.An eighth-order scheme that effectively reduces numerical dissipation in the low and middle-wavenumber regions while maintaining excellent shock-capturing ability is developed.Secondly, we review the numerical studies of the simplified models of the shockassociated noise problems of the supersonic jet.We also introduce our recent results of the numerical simulations of three-dimensional circular supersonic jet noise at three typical Mach numbers.The comparisons with the experimental results and the other numerical results from the literature validate the excellent shock-associated noise computation applicability of the modified WENO scheme.