A WEIGHTED-OPTIMIZATION COMPACT SCHEME FOR SHOCK-ASSOCIATED NOISE COMPUTATION AND ITS NONLINEAR EFFECT ANALYSIS

For the supersonic flow, the shock waves interact with the turbulent structures to generate high intensity shock-associated noise. High fidelity numerical simulation of shock-associated noise requires the shock-capturing scheme to have the properties of high-order accuracy, low dissipation and low dispersion. It is also necessary to reduce the nonlinear effect caused by the nonlinear implementation of scheme as much as possible. The existing upwind/symmetric hybrid weighted non-linear compact scheme with sixth order accuracy (called by CCSSR-HW-6 scheme, Journal of Computational Physics, 2015, 284: 133-154) introduces two-stage weighting strategy to construct the numerical flux at the cell center based on the symmetric stencil. Each stage of weighting in CCSSR-HW-6 scheme must design a nonlinear function for the weighting coefficient, which makes the nonlinear effect enhanced. In this paper, a weighted optimization compact scheme (called by WOCS scheme) is established through optimizing the nonlinear characteristics of original CCSSR-HW-6 scheme. The error integral function of modified wavenumber is chosen as the optimization objective function. The accuracy verification shows that the WOCS scheme has more than fifth order accuracy. The analysis of spectral property shows that compared to original CCSSR-HW-6 scheme, the dissipation error and the nonlinear effect of WOCS scheme are significantly reduced. Numerical experiments on several typical shock-associated noise problems show that the WOCS scheme not only improves the resolving ability of high-frequency waves, but also significantly attenuates the non-physical oscillations in numerical solution caused by the nonlinear effect.