高阶加权紧致非线性格式（WCNS）在二维流动计算中的加速收敛研究

以二维圆柱超声速无粘和粘性绕流的数值模拟为例,空间项采用高阶精度格式WCNS离散,对比研究了LU-SGS、高斯-赛德尔点松弛、线松弛以及GMRES等隐式求解方法的收敛性,并对右端项中的无粘通矢量、GMRES方法中的预处理和子迭代等影响作了对比计算.结果表明,右端项采用Steger-Warming无粘通矢量的收敛性优于其他通失量方法,采用了准确的解析雅克比矩阵的点、线松弛的收敛速度优于LU-SGS,以线松弛为预处理的GMRES算法具有良好的收敛特性.

Investigation of convergence acceleration for high-order scheme (WCNS) in 2D supersonic flows

In this paper,a number of different implicit methods are compared for 2D inviscid and viscous supersonic flows in which the high-order scheme WCNS is used for space discretization.The methods include LU-SGS,Gauss-Seidel point-relaxation,line-relaxation and GMRES preconditioned with each of the three others.The results indicate that: the inviscid flux-vector of Steger-Warming is better than the others,both the point and line relaxations with analytical Jacobian matrix converge ere faster than LU-SGS,and GMRES can obtain a higher convergence rate especially when combined with line-relaxation.