基于气动声学问题的高阶非线性紧致格式

文章基于线性中心紧致差分格式, 通过非线性加权插值的方法来求解网格中心处的函数值.这类格式保持了原有中心紧致差分格式的高阶精度和低耗散特性, 同时其分辨率也非常高, 由于其非线性插值的机制, 使得这类格式能够捕捉强激波, 所以这类新的高阶非线性紧致格式是一种较好的模拟湍流和气动声学等多尺度问题的方法. 

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.