非结构网格中LU-SGS隐式算法的非平衡性影响

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.

Effects of imbalance of LU-SGS implicit algorithm using unstructured grid

Solving the Euler equation with LU-SGS implicit algorithm on unstructured grids, mesh reordering will bring on imbalance. If the two approximately-factored items are equal, we call it balance; if not equal, it is imbalance. And it is difficult to achieve full balance we hope by mesh reordering. This paper investigates the effects of imbalance on convergence. For two- dimensional problems, two reordering methods are designed for the quadrangular-grid: One is balance and the other is imbalance. First the amplification factor of the LU-SGS implicit algorithm is analyzed for scalar function. Then we validate the effects through numerical test. The results show that balance is superior to imbalance and imbalance can also achieve convergence.