自适应的移动单位分解法求解边界层问题

An adaptive moving partition of unity method for the boundary layers problem

提出一种新的无网格方法,即自适应移动单位分解法来处理边界层问题,该方法的主要思想是将移动网格技巧与单位分解法结合起来.利用等弧长分配自适应地移动节点分布,在此基础上使用单位分解格式求解一维对流扩散模型,并给出方法的理论基础与算法流程.文中数值实验结果验证了该自适应移动方法的有效性和优越性.

A new meshless method, which is the adaptive moving partition of unity method is proposed for the boundary layers problem. Its main idea is combining the moving mesh technique with the partition of unity method. The nodal points are adaptively distributed by the equal arc-length in an iterative way, then the partition of unity scheme is applied to solve one dimensional convection-diffusion model, and the theoretical foundation and algorithmic map of this method are provided. The numerical results convincingly demonstrate the efficiency and superiority of the adaptive moving method .