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发展了一种基于广义极小残差(GMRES)算法的悬停旋翼数值模拟方法,并对GMRES算法中矩阵与向量乘积的两种计算方法进行了分析和讨论。应用该方法在旋转坐标系中采用非结构混合网格和格点格式有限体积法对以绝对速度为变量的欧拉方程进行了直接求解,其中对流项的离散应用了基于Roe的Riemann近似解的迎风格式。对Caradonna-Tung旋翼跨声速悬停流场进行了数值模拟,计算结果与相关实验数据吻合较好,并与LU-SGS方法进行了对比,表明GMRES算法可以有效地加速流场的收敛,提高计算效率。
A method of numerical simulation of hover rotor based on GMRES algorithm is developed. Two methods to calculate the product of matrix and vector in GMRES are analyzed and discussed. In this paper, Euler equations with absolute velocity as variables are solved directly by unstructured mixed mesh and lattice finite volume method in the rotating coordinate system. The Roe-based Riemann approximation solution is applied to the discretization of convection term Windy style. The numerical simulation of the transonic hover flow field in Caradonna-Tung rotor is carried out. The calculated results are in good agreement with the relevant experimental data and compared with the LU-SGS method. It shows that the GMRES algorithm can effectively accelerate the convergence of the flow field and improve the calculation effectiveness.