时间谱方法中的高效GMRES算法

发布时间：2018-06-18 18:47

本文选题：时间谱方法 + 广义极小值残差(GMRES)算法　；参考：《航空学报》2017年07期

【摘要】：研究了时间谱方法求解周期性非定常流场的计算效率,并对时间谱方法应用于周期性非定常流动的隐式求解方法进行探讨。当采样点数增加或减缩频率增大时,时间谱方法对应的雅可比矩阵对角占优性质迅速恶化,导致很多传统的迭代方法失效。为了解决上述问题,论文采用带预处理的广义极小残差(GMRES)算法来提高雅可比系数矩阵的计算收敛性。使用时间谱方法对NACA0012翼型强迫振荡算例进行计算,并与时域差分方法的计算效率和精度进行对比。研究表明在保证计算精度的同时,时间谱方法普遍可将计算效率提高一个量级左右。对于跨声速周期性流动,广义极小残差算法不论是稳定性还是收敛性都优于对称SGS迭代算法。
[Abstract]:The computational efficiency of time spectrum method for solving periodic unsteady flow field is studied, and the implicit solution of periodic unsteady flow using time spectrum method is discussed. When the sampling number increases or the reduction frequency increases, the diagonally dominant property of the Jacobian matrix corresponding to the time spectrum method rapidly deteriorates, which results in the failure of many traditional iterative methods. In order to solve the above problems, the generalized minimal residuals (GMRESs) algorithm with preprocessing is used to improve the convergence of Jacobian coefficient matrix. The time spectrum method is used to calculate the forced oscillation of NACA0012 airfoil, and the computational efficiency and accuracy are compared with that of the time-domain difference method. It is shown that the time spectrum method can improve the computational efficiency by about one order of magnitude while ensuring the accuracy of the calculation. For transonic periodic flow, the generalized minimal residual algorithm is superior to the symmetric SGS iterative algorithm in terms of stability and convergence.
【作者单位】：西北工业大学航空学院;郑州航空工业管理学院航空工程学院;
【基金】：国家自然科学基金优秀青年基金(11622220) 高等学校创新引智计划(B17037)~~
【分类号】：O241.8

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