瞬态热传导问题的无网格局部Petrov-Galerkin法

基于加权余量法和采用移动最小二乘近似函数作为试函数,研究了无网格局部Petrov-Galerkin方法在瞬态热传导问题中的应用.阐述了该方法应用于瞬态热传导问题的过程和基本理论,并编制了相应的计算程序进行计算.算例表明该方法用来求解瞬态热传导问题是有效的.

A Meshless Local Petrov-Galerkin Method for Transient Heat Conduction Problems

The meshless local Petrov-Galerkin method is extended to solve the transient heat conduction based on the weighted residual method and the moving least square approximation used to interpolate solution variables.The weighted function of the moving least square approximation is chosen as a test function of the weighted residual method.The present method is an effective meshless one because it doesn't need any mesh or background while all integrals can be easily evaluated over regularly shaped domains and their boundaries.In the test,the essential boundary conditions are enforced by a penalty method.The basic theory and numerical implementation of the local Petrov-Galerkin method for solving transient heat conduction problem and its corresponding computer program are developed.This method for transient heat conduction problems is proved valid and efficient.