一种基于AUSM思想的通量分裂方法

A Flux Splitting Scheme Based on AUSM

根据对流迎风分裂(AUSM)思想提出一种通量分裂方法,称为K-CUSP格式.它与传统H-CUSP和E-CUSP格式的最大差异在于总能量的分裂:K-CUSP格式将无粘守恒通量中所有的运动学量分裂到对流项,所有的热力学量分裂到压力项,即总能量被分裂成动能和静焓.对于压力项的数值通量,采用一种新的界面构造方法.数值测试表明:1K-CUSP格式继承了FVS格式的简单性和稳健性.在激波后不易出现压力过冲,在膨胀区域没有振荡,优于AUSM和WPS格式;2K-CUSP格式继承了FDS格式的分辨率.激波间断的分辨率和H-CUSP、E-CUSP格式基本相同,接触间断的分辨率高于FVS格式,低于Roe、AUSM和WPS格式.AUSM和WPS格式在计算运动接触间断时,速度存在很大振荡,而新格式不存在振荡.

According to advection upstream splitting method, a flux splitting method called K-CUSP is proposed. The greatest difference between K-CUSP and two traditional CUSP schemes, namely H-CUSP and E-CUSP, is splitting of total energy： All kinematic quantities and thermodynamic quantities should be separately split into convective term and pressure term by K-CUSP scheme. Numerical tests indicate that：① K-CUSP scheme inherits the simplicity and robustness of FVS scheme. It is less prone to pressure overshoot after shock and no oscillations in expansion area, which is better than AUSM and WPS schemes. ② K-CUSP scheme also inherits resolution of FDS scheme. Shock resolution is almost the same with H-CUSP and E-CUSP schemes. Contact discontinuity resolution is better than FVS schemes, a little worse than Roe, AUSM and WPS schemes. However, velocity of contact discontinuity in AUSM and WPS schemes exist large oscillation, while our scheme does not.