求解可压缩流的二维通量分裂格式

A two-dimensional flux splitting scheme for compressible flows

传统的一维通量分裂格式在计算界面数值通量时,只考虑网格界面法向的波系。采用传统的TV格式分别求解对流通量和压力通量。通过求解考虑了横向波系影响的角点数值通量来构造一种真正二维的TV通量分裂格式。在计算一维数值算例时,该格式与传统的TV格式具有相同的数值通量计算公式,因此其保留了传统的TV格式精确捕捉接触间断和膨胀激波的优点。在计算二维算例时,该格式比传统的TV格式具有更高的分辨率;在计算二维强激波问题时,消除了传统TV格式的非物理现象,表现出更好的鲁棒性;此外,该格式大大提高了稳定性CFL数,从而具有更高的计算效率。因此,本文方法是一种精确、高效并且具有强鲁棒性的数值方法,在可压缩流的数值模拟中具有广阔的应用前景。

Traditional one-dimensional flux splitting schemes only consider the waves orthogonal to the cell interface when computing the numerical flux.The convective flux and pressure flux are determined by the traditional TV scheme.A genuinely two-dimensional TV flux splitting scheme is proposed by solving the numerical flux at the corner which considers the effect of transverse waves.The numerical flux of this scheme is the same as that of the traditional TV scheme when computing one-dimensional numerical examples.So,it preserves the merits of the traditional TV scheme,such as,capturing contact discontinuity and expansion shock waves accurately.It has a higher resolution than the traditional TV scheme when computing two-dimensional numerical examples and eliminates the unphysical shock anomaly in solving two-dimensional strong shock wave problems,displaying better robustness.In addition,this scheme increases the stable CFL number greatly,having higher computational efficiency.Therefore,it is an accurate,efficient and robust numerical method,which has a broad application prospect in the numerical simulation of compressible flow.