一类新型激波捕捉格式的耗散性与稳定性分析

高超声速流动是高复杂性的可压缩黏性流动, 其中存在激波、剪切层、激波/激波干扰、激波/边界层干扰、旋涡与分离流动等复杂流场结构. 对其进行准确模拟需要使用低耗散、强鲁棒性的激波捕捉方法. 本文基于一类新型的通量项分裂方法, 提出了一种耗散低且鲁棒性好的激波捕捉格式K-CUSP-X. 对该格式的耗散性和激波稳定性进行了详细的理论分析, 得到了格式激波稳定的数值条件. 推论认为, 迎风格式激波稳定的充分条件为速度扰动量具有衰减性, 数值实验验证了该推论. 研究表明, 该格式与Toro提出的通量分裂格式K-CUSP-T相比, 在保证精确捕捉接触间断的同时, 又具有更好的稳定性, 在激波处不会产生“红玉”现象.

On the accuracy and robustness of a new flux splitting metho d

The high speed flow problems usually involve complex flow phenomena, such as strong shock waves, shock-shock interactions, and shear layers. Prediction of these problems requires robust, efficient and accurate numerical methods. A robust flux splitting method capable of capturing crisp shock profile and exact contact surface is presented. Here, the flux vector of the Euler equation is split into convective and pressure parts according to the Toro''s formulation. The accuracy of the numerical method at the contact discontinuity is examined first. Sufficient conditions of shock stability for this new method are obtained through a linear perturbation analysis. Several carefully chosen test problems are numerically investigated, and the numerical results demonstrate the accuracy and robustness of the proposed scheme.