一种参数化曲面网格生成方法

针对在计算机辅助设计(CAD)及流场数值计算中,经常遇到绘制曲面及曲面网格的问题,探讨了一种生成参数化曲面网格的新方法.介绍的参数化曲面网格生成方法是依据代数变换和椭圆变换得来的.通常所用的二维和三维域椭圆变换是基于在Laplace方程,而本文生成的参数化曲面网格,则基于Laplace beltrami方程.由代数变换和椭圆变换构成的复合变换服从Possion方程的椭圆系统,其控制函数由代数变换确定,且遵守Neumann边界条件,这就保证了网格边界上的正交化.该方法生成的网格最终由曲面本身的形状及边界上的网格点分布确定,减少了计算量,尤其对大型复杂型面可有效提高网格生成速度.

An approach for parameterized grid generation

In the progress of CAD and flow field calculation, a common problem is protecting the curvilinear surface and curvilinear grid generation. A new method of generating a parameterized grid is based on the interactive algebraic and elliptical method. In general, in terms of the two- dimensional and three-dimensional regions, the elliptical method is based upon the Laplace equation.Yet,in terms of the parameterized grid generation, it is based on the Laplace-Beltrami equation. This multiple way combined with the interactive algebraic and elliptical system, submits to the Possion equation .The manipulative function was confirmed by the interactive algebraic method, and it obeyed Neumann boundary condition,making sure that the curvilinear grids near boundaries are orthogonaes. The way shows that the final grid only on the shape of the surface mesh and distribution of boundary mesh. This method of grid generation can reduce the time of grid generation, especially for a large surface, and can increase the speed of complicated grid generation.