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ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 2014, Vol. 35 ›› Issue (5): 1181-1192.doi: 10.7527/S1000-6893.2013.0430

• Fluid Mechanics and Flight Mechanics • Previous Articles     Next Articles

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

YAN Zhenguo1, LIU Huayong1, MAO Meiliang1,2, DENG Xiaogang3, ZHU Huajun1   

  1. 1. State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China;
    2. Institute of Computational Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China;
    3. National University of Defense Technology, Changsha 410073, China
  • Received:2013-06-25 Revised:2013-10-12 Online:2014-05-25 Published:2013-11-16
  • Supported by:

    National Natural Science Foundation of China (11072259); National Basic Research Program of China (2009CB723801)

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: