关键词: 网格生成, 偏微分方程, 正交性, 数值方法

Abstract:

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.

Key words: grid gener ation, partial differential equation, orthogonality, numerical methods