基于高阶耗散紧致格式的GMRES方法收敛特性研究

doi:10.7527/S1000-6893.2013.0430

Abstract

Abstract:

Low computational efficiency is an important factor constraining the application of high-order numerical methods. To improve the computational efficiency of hybrid cell-edge and cell-node dissipative compact scheme (HDCS), a generalized minimum residual (GMRES) algorithm suitable for multi-block structured grids is developed to accelerate simulations. The influence of GMRES's precondition methods, CFL number and sub-iteration number on convergence property of HDCS high-order simulations is investigated. It is shown that the point relaxation method is an efficient precondition method, that the CFL number can greatly affect the computational efficiency, and that GMRES has an optimal sub-iteration number. GMRES is applied to simulations of NACA 0012 airfoil, NLR 7301 airfoil and DLR-F4 wing/body configuration, and is compared with other implicit time integration methods. By using GMRES, the computation becomes more stable, and the computational efficiency can be improved by more than 5 times when compared with the LU-SGS(Lower-Upper Symmetric Gauss-Seidel) method. The results indicate that the GMRES method developed in this paper has good stability in multi-block structured grids, the residual can converge to lower levels, and GMRES can greatly improve the computational efficiency of high-order simulations.

Key words: implicit time integration method, numerical methods, high-order scheme, HDCS, GMRES, convergence property, computational efficiency

CLC Number:

V211.3
O355

YAN Zhenguo, LIU Huayong, MAO Meiliang, DENG Xiaogang, ZHU Huajun. Convergence Property Investigation of GMRES Method Based on High-order Dissipative Compact Scheme[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(5): 1181-1192.

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Convergence Property Investigation of GMRES Method Based on High-order Dissipative Compact Scheme

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