一种基于求解椭圆型方程的结构动网格生成方法

摘要

基于椭圆型网格生成法,实现了一种简单高效的贴体结构动网格生成方法,可用于具有移动边界问题的非定常流动数值模拟.该方法提出,在网格变形过程中,Poisson方程需要的控制网格间距和正交性的源项可以通过提取已知的静态网格源项直接得到,并在整个动网格生成过程中保持不变.因此,在椭圆型网格生成中需要通过外迭代确定源项的过程可以得到省略,而且该方法不需要人工指定参数.这使得方法具有高效和易于嵌入到已有程序中的特点.数值模拟结果证明,采用这种方法获得的网格能够较好地保持静态网格原有的正交性和光滑性,在相同迭代步数约束下,网格求解效率低于传统弹簧模拟法,但鲁棒性优于弹簧模拟法.%A simple robust structured dynamic grid generation method based on the solution of elliptic partial differential equations is developed for computing the unsteady flows with moving boundaries.In the method,the source terms of the Poisson equation which can control the spacing and the orthogonality of the grid are inherited from the known static grid,and held fixed throughout the process of dynamic grid generation.With the process,the outer iterations for determining the source terms usually needed in the elliptic grid generation can thus be saved,and no adjustable parameters are required to be prescribed.This makes the method more efficient and easy to implement in an existing CFD code.The numerical results demonstrate that the proposed method can provide an efficient way of deforming the grid based on solving elliptic partial differential equations.The orthogonality and smoothness of original static grid can be maintained well by the proposed method.When the same number of iterations are given as the constraint condition,the grid generation efficiency of the method is lower than that of the spring analogy,but the robustness of the method is superior to the spring analogy.