时动边界上热传导问题的求解方法

A Method of Moving Boundary in Heat Conduction Problem

有Neumann边界条件的抛物型方程的初边值问题是偏微分方程研究领域的一类经典的问题。这是由已知的边界条件和初始条件来求区域温度场的问题。若所给边界是固定区域的称为定边界问题,而现实中又有一类问题其边界随时间变化,这样的问题称为动边界问题。文章对于时动边界上的热传导问题的求解提出人工边界的方法,并在人工边界的基础上采用了差分方法求解此定解问题。为了检验方法的可行性,给出了数值模拟。

The initial boundary value problem for parabolic equation with Neumann boundary condition is a kind of classical problem in partial differential equations.The direct problem is to determine the temperature field from given initial and boundary conditions.Compared with the fixed boundary problem,there is another boundary problem of movingboundary.In this paper we use the artificial boundary to solve the moving boundary problem.The difference method is used to deal with this problem.Numerical results are given to support the proposed schemes.