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在非结构网格中用LU SGS隐式算法求解欧拉方程时,两个近似分解因子的项数可能相等,为平衡;也可能不相等,为非平衡。采用对网格重新编号的方法很难达到我们希望的平衡。本文对非平衡性的影响进行了探讨。对二维问题,四边形单元的非结构网格,设计出平衡与非平衡的编号方式。先对标量模型方程分析LU SGS隐式算法的增长因子,然后通过数值试验来验证这种非平衡性的影响。结果表明,尽管非平衡时也能达到收敛,但平衡却远优于非平衡的情况。
When LU Euclidean equation is solved by LU SGS implicit algorithm in unstructured grid, the number of two approximate decomposition factors may be equal, balanced or unequal, and may be unbalanced. It’s hard to get the balance we want with the renumbering of grids. This article explores the impact of non-equilibrium. For two-dimensional problems, unstructured grids of quadrilateral elements, a balanced and unbalanced numbering scheme is designed. First, we analyze the growth factor of LU SGS implicit algorithm for scalar model equations, and then verify the effect of this non-equilibrium by numerical experiments. The results show that although the convergence can be achieved even in non-equilibrium, the balance is far better than the non-equilibrium.