稳定性可保证二阶格式在多重网格中的有效性和经济性

基于一种稳定性可保证的二阶差分格式（SGSD），对SIMPLE算法实施了完全多重网格循环以加速外迭代的收敛．采用规正变量的方法实施了SGSD．通过对二维顶盖驱动流动的计算，分析了多重网格在SIMPLE算法中的收敛特性．计算结果表明：SGSD格式具有与其他高阶格式及高阶组合格式相同的计算精度，且收敛速度优于其他高阶格式，在雷诺数较高时（Re=3000），其收敛速度是二阶迎风格式的1．77倍，是QUICK格式的1．37陪，同时在疏密网格层次上均可以保证计算的稳定性；采用多重网格加速SIMPLE算法的迭代时，不仅要考虑多重网格的循环方式，还要考虑对流项的离散格式，在计算中SGSD格式具有明显的优势。

Efficiency and Accuracy of Stability-Guaranteed Second-Order Difference Scheme in Full-Multigrid Method

Based on a new stability-guaranteed second-order difference (SGSD) scheme, the full multigrid cycle was implemented in SIMPLE algorithm in order to accelerate convergence of outer-iteration. The difference scheme was implemented by using normalized variable method. The convergence characteristics of full multigrid cycle in SIMPLE algorithm were analyzed by numerical simulation of 2D lid-driven cavity flow. The results show that the SGSD scheme can reach second-order accuracy compared with other high-order schemes and the convergence rate is higher than that of other schemes. The convergence rate of SGSD is 1.77 times that of second-order upwind difference scheme and 1.37 times that of QUICK scheme with Re=3 000, and the stability can be guaranteed in coarse or fine grid. When the multigrid technique is adopted to accelerate the convergence rate, both the circulation pattern and the discretization scheme of convection term should be taken into account. In this regard, the SGSD scheme has an obvious advantage for multigrid implementation.