数值网格生成技术中方程非线性系数对网格正交性和疏密分布的影响

对椭圆型方程中非线性系数对网格正交性和空间分布的影响进行了理论分析和数值验证。结果表明 :方程中混合偏导数项系数具有控制网格正交性的作用;其它两个二次偏导数项系数具有调节网格空间分布的作用,且其调节的强弱和作用与其比值有直接关系。利用方程系数的这些特性,提出一种 Numman边界条件的给定方法,较好地实现了网格正交和疏密分布的有效控制。

EFFECTS OF NON-LINEAR FACTORS IN NUMERICAL GRID GENERATION EQUATIONS ON ORTHOGONALITY AND SPACING

The numerical grid generation techniques using PDE are widely used practically and studied frequently. In this paper the non linear factors in the elliptic equations for grid generation are studied in details. The theoretical and numerical results show that the factors have strong influences on the grid spacing and orthogonality. The factor of the mixed partial derivative term controls the grid orthogonality. The other two factors of second order partial derivative terms control the grid spacing. The strength and function of spacing controlling are directly connected with the ratio of the factors. Based on the above characteristics of the factors with a Numman boundary condition, the orthogonality and spacing distribution of grid can be well controlled. These results have also a significant impact for both the parabolic and hyperbolic equations.