适用于气动学问题的DRP类有限差分方法

研究了一类低耗散低色散的高阶精度有限差分方法,目的是直接计算非定常欧拉方程用于气动声学问题.采用的数值方法是空间四阶、时间三阶精度的色散关系保持(DRP:dispersion-relation-preserving)类有限差分格式,通过波动方程算例验证了格式模拟波动问题的能力;采用加变幅值的高波数人工耗散项来抑制高频数值振荡,使得该格式可推广用于含激波、初始间断或非线性波动的问题.通过含激波、初始间断条件的算例验证了所用变幅值人工耗散的有效性,最后作为初步应用计算了二维亚、超音速均匀流中简单点声源辐射问题,得到了很好的结果,表明此类方法在气动声学问题计算上深有潜力.

A type of DRP finite difference schemes for aeroacoustic problems

A type of dispersion-relation-preserving (DRP) finite difference scheme is studied for aeroacoustic applications. The scheme used here has four order accuracy in spatial and three order accuracy in temporal. Its accuracy in simulation of wave motion is demonstrated by a few numerical tests. With a variable-coefficient high wave-number damping term, this scheme could be extended to more complicated cases involving nonlinear oscillations or discontinuities. The effectiveness of the scheme with artificial damping is demonstrated by one- and two-dimensional numerical tests involving a shock waves and initial discontinuities. The radiation of a point source in a subsonic and supersonic uniform mean flows is investigated, with good results obtained, showing that the method could be used for more complicated aeroacoustic applications.