基于压力间断解析解对AUSM -up格式的修正*

AUSM -up格式是AUSM类系列格式中最完善的,通过在对流通量中引入压力耗散,同时在压力通量中引入速度耗散,使之在各种马赫数下均有良好的收敛性和稳定性。然而,通过对格式的分析,我们发现当马赫数为零时,在压力间断位置会出现质量通量无穷大的非物理现象。为了克服这一缺陷,采用特征线法获得了压力间断问题的解析解；以此为基础,对对流通量中的压力耗散项进行修正,发展出新的AUSM -up格式。以新的格式对不同速度驱动下的冲击波发展、不同强度压力间断问题和激波衍射问题进行了仿真,计算结果与理论解吻合得较好。

A Modified AUSM[sup_s] [sup_e]-up Scheme Based on the Analytic Solution of Pressure Discontinuity

AUSM -up scheme is one of the most perfect schemes of ASUM-family. By introducing pressure dissipative mechanism into the convective fluxes and velocity diffusion into pressure fluxes, the convergence and robustness are remarkably improved in all Mach number regimes. However, based on an analysis of the scheme, we find that when the Mach number is zero, a nonphysical phenomenon of infinite mass flux emerges. For conquering the imperfection, the analytic solution of pressure discontinuity is obtained by characteristic method. According to the results, the item of pressure dissipation is modified, and a new AUSM -up scheme is developed. Using the new scheme, the strong discontinuity problems of shock wave, pressure discontinuity and shock wave diffraction are simulated. The Calculation results fit the theory results well.