用加权最小二乘无网格法求解稳态热传导问题

Meshless Weighted Least-Square Method for Stable Heat Conduction Problems

加权最小二乘无网格法是一种新的高效无网格法。该方法除节点外又引入了一些辅助点,控制方程在所有节点和辅助点处的残差用最小二乘法予以消除,边界条件用罚函数法引入。将加权最小二乘无网格法应用于求解稳态热传导问题,编制相应的计算程序进行计算,并通过算例表明该方法是有效的。

Meshless Weighted Least Square Method (MWLS) is a new efficient method. Except for nodes, a number of auxiliary points are used to eliminate the residual of governing equations by weighted least square method. The boundary conditions are imposed by using the penalty method. In this paper, this method is used to solve stable heat conduction problems and the corresponding computer program is developed. As a result, the method used in this paper proves to be valid and efficient.