无单元Galerkin法在热传导中的应用

对热传导问题的微分方程采用无单元Galerkin法进行数值求解.首先,将微分方程用Galerkin加权残量法转化为等效的积分形式.然后,先将时间变量看作参数,对空间变量进行离散化,得到方程的半离散形式,接着,对时间采用向后Euler—Galerkin格式进行离散,得到方程的全离散形式最后,编制MATLAB程序,上机计算.列举了两个热传导算例,通过计算说明EFG法适用于热传导问题,且其计算速度快,精确度高、前后处理也十分方便,是一种具有潜力的温度场数值计算的新方法.

Element Free Galerkin Method for Heat Exchange

In this paper,the equation of heat conduction problem was numerically solved by element Free Galerkin Method(EFG).First,the differential equation was converted into an equivalent integral form by Galerkin weighted residual method.Then,will first time variables as parameters,the spatial variables discretization,get half the discrete equation of the form,then to discrete time using backward Euler-Galerkin scheme,get the discrete form of equation.Finally,the MATLAB program,the computer calculation.This paper enumerates the two heat transfer calculation,through calculation,EFG method is suitable for the heat conduction problem,and the calculation speed,high precision,before and after the treatment is also very convenient,is a kind of new method for the numerical simulation of temperature field has the potential.