一种同位网格上的迎风Galerkin有限元方法

A Co-Located Upwind Scheme-Based Galerkin Finite Element Method

通过 Green定理将对流项变量从微分算子中分离出来 ,从插值函数入手引入迎风格式 ,是对强对流问题 Galerkin有限元计算中对流项变量的一种新的处理方法。按这种方法采用局部斜迎风格式及速—压同位网格公式 ,构成了一种对高 Reynolds数流体流动数值模拟比较有效的有限元方法。数值试验表明 ,采用该方法能较好地提高计算精度。

Invoking Green's theorem to separate the convection variable from the differiential operator of weighted residual equation is a new strategy of using upwind scheme in Galerkin finite element method. As an example, the locally skewed upwind scheme is proposed. By imple-menting this strategy in conjunction with the equal-order velocity-pressure formulation, the convection-dominated fluid flow can be obtained more accurate simulation in complex geometrics. This paper not only has established this new method, but also has proved its accuracy is rather encouraging by its application to some typical examples and comparisons with other literatures.