一种激波稳定的对流-压力通量分裂格式

A new shock stable convection-pressure flux splitting scheme

针对欧拉方程三种流行的对流-压力通量分裂方法(Liou-Steffen,Zha-Bilgen和Toro-Vázquez)进行特征分析,进而提出一种新的对流-压力通量分裂格式。采用Zha-Bilgen分裂方法将欧拉方程的通量分裂成对流项和压力项两部分,使用TV格式来计算这两部分的数值通量。利用压力比构造激波探测函数,并且在强激波附近的亚声速区域增加TV格式的剪切粘性来克服数值模拟中的激波不稳定性。数值算例的计算结果表明,新的对流-压力通量分裂格式不仅保留了原始TV格式精确分辨接触间断的优点,而且具有更好的鲁棒性,在数值模拟多维强激波问题时不会出现不稳定现象。因此,该格式是一种精确并且具有强鲁棒性的数值方法,可以广泛地应用于可压缩流体的数值计算中。

As for the Euler equations,the characteristics analyses of three popular convection-pressure flux splitting methods(Liou-Steffen,Zha-Bilgen and Toro-Vázquez)are conducted.Then a new convection-pressure flux splitting scheme is proposed,and the numerical fluxes of these two parts are computed by the TV scheme.A shock-detection function is defined by the ratio of pressure,and the shear viscosity is added to the TV scheme in the subsonic region near the strong shock to overcome the shock instability in the numerical simulations.The computational results of numerical examples show that the new convection-pressure flux splitting scheme not only retains the advantage of capturing contact discontinuity accurately but also is more robust than the original TV scheme,eliminating the instability in numerical simulation of multi-dimensional strong shock wave problem.Therefore,it is an accurate and robust numerical method,which can be widely used in the numerical computation of compressible flow.