RK-AUSM^+混合格式在跨声速Euler方程计算中的应用

RK-AUSM~＋ Schemes Applied to Transonic Euler Equations Solution

首先在一维AUSM＋格式的基础上，推导出了AUSM＋格式在任意曲线坐标下的二维形式，并将其与Runge-Kutta格式结合，对跨声速Euler方程进行求解。最后，为了验证RK-AUSM＋混合格式的有效性，将典型双圆弧叶栅无粘跨声速流动作为算例。本文计算结果和文献结果符合很好。

In this paper, an AUSM+ schemes is developed for the multidimensional hyperbolic conservation laws in curvilinear coordinates. The present scheme combined with the Runge-Kutta scheme is applied to transonic Euler equations solution. In order to examine the accuracy of the RK-AUSM+ schemes, two-dimensional transonic flow through the cascade built of two circular arc blades is computed. The computed results is compared with the other computed results and good agreement between them is obtained. The results given in this paper show that the present scheme possess obvious superiority in aspects of convergence rate, accuracy and robustness for calculating transonic flow fields compared with CD scheme, and there is no any spurious oscillation near the shock wave.