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计算效率较低是当前限制高阶精度计算方法应用的重要因素。为了提高高阶精度混合型耗散紧致格式(HDCS)的计算效率,发展了适合多块对接网格的广义最小残值(GMRES)方法,并利用GMRES方法开展了HDCS格式的加速收敛研究。首先研究了GMRES的预处理方法、CFL数和内层迭代步数对HDCS数值模拟收敛特性的影响,计算结果显示:点松弛方法是一种高效的预处理方法;CFL数对计算收敛速度影响较大;GMRES方法存在最优的内层迭代步数。利用GMRES方法完成了NACA 0012翼型绕流、NLR 7301翼型绕流和DLR-F4翼身组合体绕流的数值模拟,并与其他隐式时间推进方法进行了对比,GMRES方法计算更加稳定,并且计算效率相对LU-SGS(Lower-Upper Symmetric Gauss-Seidel)方法可以提高5倍以上。研究结果表明,本文发展的GMRES方法在多块对接网格中具有良好的计算稳定性,计算结果的残差可以收敛到更低的量级,并且可以较大幅度地提高高阶精度数值模拟的计算效率。
The low computational efficiency is an important factor that limits the application of high-order precision calculation methods. In order to improve the computational efficiency of high-order hybrid compact dissipative compact format (HDCS), a generalized minimum residuals (GMRES) method for multi-patch butt-meshes is developed. The GCRES method is used to study the accelerated convergence of HDCS format. The effects of GMRES preprocessing method, CFL number and internal iteration steps on the convergence of HDCS numerical simulation are studied. The results show that the point relaxation method is an efficient preprocessing method. The influence of CFL number on the convergence rate The GMRES method has the best number of inner iteration steps. The numerical simulation of the flow around the NACA 0012 airfoil, the NLR 7301 airfoil and the DLR-F4 airfoil body was completed by the GMRES method. Compared with other implicit time propulsion methods, the GMRES method is more stable, Compared with the LU-SGS (Lower-Upper Symmetric Gauss-Seidel) method, the computational efficiency can be improved more than 5 times. The results show that the GMRES method developed in this paper has good computational stability in multiple patch grids, and the residuals of the calculated results can converge to a lower magnitude, and can greatly improve the precision of high-order numerical simulation Computational efficiency.