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本文给出了绕二维与三维刚性或弹性振动机翼非定常无粘流动的欧拉方程解。首先利用Ｊａｍｅｓｏｎ的有限体积方法建立了求解欧拉方程的Ｒｕｎｇｅ－Ｋｕｔｔａ方法。为了提高受Ｒｕｎｇｅ－Ｋｕｔｔａ法稳定性限制的时间步长，文中采用了变系数的残值光顺方法。该方法避免了常系数残值光顺引起局部流场损失较大的问题。同时可在保证原计算格式精度要求下，大幅度提高计算时间步长，从而提高了计算效率。文中以二维与三维矩形机翼为例，分别对其在跨音速流场中作则性或弹性振动的非定常气动力进行了计算，研究了不同振动频率对流动产生的影响。部分计算结果与相应实验结果进行了比较。结果证明本方法是可靠的，可以用于求解绕任意运动机翼非定常流动问题。
In this paper, we present the Euler equations for unsteady and non-viscous flow around two-dimensional and three-dimensional rigid or elastic vibrating wings. Firstly, Runge-Kutta method for solving Euler equations is established by Jameson’s finite volume method. In order to improve the time step limited by the stability of Runge-Kutta method, the variable coefficient saliency method is adopted in this paper. This method avoids the problem of large loss of local flow field caused by the smoothness of constant coefficients. At the same time, it can greatly improve the calculation time step while ensuring the accuracy of the original calculation format, so as to improve the calculation efficiency. Taking two-dimensional and three-dimensional rectangular wings as an example, the unsteady aerodynamic forces acting normal or elastic vibration in the transonic flow field are calculated respectively. The effects of different vibration frequencies on the flow are studied. Some calculated results are compared with the corresponding experimental results. The results show that this method is reliable and can be used to solve the unsteady flow around any moving wing.