一种适用于三维混合网格的GMRES加速收敛新方法

发布时间：2018-06-06 20:23

本文选题：混合网格 + 收敛效率　；参考：《航空学报》2016年11期

【摘要】：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。
[Abstract]:In order to improve the convergence efficiency of flow field computation, a set of parallel generalized minimum residuals (GMRES) implicit time advance method for solving Naiver-Stokes equations with three-dimensional hybrid grids is developed. The method is implemented by Krylov subspace solver in the portable extensible tool kit (PETSc), and the coefficient matrix in linear equation system is given directly in order to improve the stability of the algorithm. To further improve the convergence rate of the GMRES method, the ordinal number of the unstructured grid is reordered to make the non-zero elements of the coefficient matrix as close as possible to the main diagonal. Using the developed GMRES method, the calculation results of the general research model CRM for the AIAA resistance prediction conference of the ONERAM6 wing have been completed. The calculated results are in good agreement with the experimental results. By comparing with other implicit propulsion methods, the convergence characteristics of the algorithm are studied. The results show that the GMRES method developed in this paper is more stable, and the reduction speed of the residual error is faster than that of the LU-SGSer-Upper symmetric Gauss-Seidel-based method, especially the velocity of aerodynamic coefficients approaching to the convergent solution is more obvious, and the computational efficiency is improved.
【作者单位】：中国空气动力研究与发展中心计算空气动力研究所;
【分类号】：V211

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