一种适用于三维混合网格的GMRES加速收敛新方法

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ONERA-M6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。

A new method to accelerate GMRES's convergence applying to three-dimensional hybrid grid

To improve the convergence efficiency of solving the flow field, a parallel implicit time integration method generalized minimal residual (GMRES) is applied to a three-dimentional hybrid grid Navier-Stokes solver. The method is implemented based on a Krylov subspace solver in the scientific computation toolkit portable, extensible toolkit for scientific computation (PETSc). The coefficient matrix of linear system is provided explicitly to stabilize the scheme. In order to accelerate the convergence more specifically, the cell indexes of unstructured grid are reordered such that the system matrix's nonzero elements are clustered close to the main diagonal. The method is applied to simulations of ONERA-M6 wing and AIAA Drag Prediction Workshop model CRM. The results show great agreement with experimental data. Comparisons are made between different implicit schemes. The GMRES method developed in this paper shows more robustness and the residual's convergence has a significant speedup compared with LU-SGS method. Moreover, the method has a faster speed approximating to the steady state of aerodynamic coefficient. It greatly improves the computational efficiency.