High Order Nonlinear Compact Schemes for Aeroacoustics

A class of nonlinear compact schemes was developed which based on previous linear central compact schemes with spectral-like resolution. In the approach, the flux derivatives on the cell-nodes by the physical fluxes on the cell nodes and numerical fluxes on the cell centers were computed. To acquire the numerical fluxes on the cell centers, a weighted nonlinear interpolation was performed. Systematic analysis and numerical tests show that nonlinear compact scheme has high order, high resolution and low dissipation, and has the same ability to capture strong discontinuities as regular weighted essentially non-oscillatory (WENO) schemes. It is a good choice for the simulation of multiscale problems with shock waves.