A seventh-order accurate weighted compact scheme for shock-associated noise computation

Abstract

High-fidelity computation of shock-associated noise places stringent requirements on the accuracy, linear and nonlinear spectral properties of shock-capturing scheme. In this paper, a novel weighted nonlinear compact scheme with seventh-order accuracy is developed for the purpose of improving the linear and nonlinear spectral properties of original scheme (Zhang et al., (2008) [1]). The numerical fluxes at cell centers are obtained using upwind-biased weighted nonlinear interpolation based on the new S-type smoothness indicator that be constant for sine and cosine functions (Wu et al., (2020) [2]). Through systematic spectral analysis and numerical experiments, it is demonstrated that the newly proposed scheme has very weak nonlinear effect and reduces the dissipation and dispersion at the medium and high wavenumbers. The resolution for the short waves and the fine-scale structures is improved. It has the potential to become a suitable candidate for the computation of shock-associated noise.