低马赫数不可压流动中声速与流速大小差别巨大,采用基于可压缩流动控制方程的计算格式求解流场时,由于数值黏性的污染,解的精度低且收敛性差,通常可使用时间预处理技术来解决这一问题。在基于控制理论的优化方法中,共轭方程的Jacobian矩阵和流动方程的系数矩阵相似,因而在低流动马赫数下,求解共轭方程存在着与求解流动方程相同的数值污染和数值刚性问题。首先推导了带有预处理的Roe格式,然后发展了适合全速度流动的共轭方程求解方法,最后选取翼型和叶栅两个典型算例进行了验证。计算结果表明所发展的方法可很好地用于低马赫数时的气动反问题设计。
Because of the large disparity between the acoustic wave speed and the waves convected at fluid speed, the accuracy of the solution to the flow fields of non-compressible low Mach number flows is poor and the convergence rate is bad when using the standard convective scheme based on compressible flows. Generally the preconditioning techniques are used to deal with this problem. In the optimization method based on control theory, the Jacobian matrix of adjoint equations and the mxatri of flow equations are similar, so the same difficulties such as oversized numerical viscosity and numerical rigidity exist when solving the adjoint equations. In this paper, a Roe scheme with preconditioning is first deduced. Then a full speed numerical scheme is developed for adjoint equations. Finally, two typical tests about an airfoil and a cascade are presented. The results indicate that the preconditioned adjoint equation method can develop a low Mach number aerodynamic inverse design efficiently.
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