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为提高流场计算收敛效率,发展了一套适用于三维混合网格Naiver-Stokes方程求解的并行广义最小残差(GMRES)隐式时间推进方法。该方法由科学计算可移植扩展工具包(PETSc)中的Krylov子空间求解器实现,线性方程系统中的系数矩阵直接以显式给出以提高算法的稳定性。为进一步提高GMRES方法的收敛速度,对非结构网格的序号进行了重排序,使得系数矩阵的非零元素尽量向主对角线靠近。利用所发展的GMRES方法,完成了对ONERAM6机翼、AIAA阻力预测会议通用研究模型(CRM)等算例的计算,计算结果与试验结果吻合良好。通过与其他隐式推进方法进行比较,对算法的收敛特性进行了研究。结果表明,所发展的GMRES方法计算更加稳定,残差下降速度相对LU-SGS(Lower-Upper Symmetric Gauss-Seidel)方法更快,尤其是气动力系数向着收敛解逼近的速度更加明显,提高了计算效率。
In order to improve the convergence efficiency of the flow field, a parallel generalized minimum residual (GMRES) implicit time-based method for solving the Nai-Stokes equations of three-dimensional hybrid grid is developed. The method is implemented by Krylov subspace solver in PETSc, and the coefficient matrix in linear equation system is given directly to improve the stability of the algorithm. In order to further improve the convergence rate of GMRES method, the sequence numbers of unstructured grids are reordered so that the non-zero elements of the coefficient matrix approach the main diagonal as far as possible. By using the developed GMRES method, the calculation of the ONERAM6 wing and the AIAA General Resistance Prediction Conference Model (CRM) was completed. The calculated results are in good agreement with the experimental results. By comparing with other implicit methods, the convergence of the algorithm is studied. The results show that the developed GMRES method is more stable and the rate of residual descent is faster than the Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method, especially the aerodynamic coefficient approaches the convergent solution more quickly, effectiveness.