时动边界上热通量重构正问题求解方法  

Methods of moving boundary in heat conduction direct problem

作　　者：张雪艳[1] 顾大权[1] 黄伟[1] 

机构地区：[1]解放军理工大学气象学院,211101

出　　处：《中国科技信息》2010年第8期43-47,共5页China Science and Technology Information

摘　　要：具有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。正问题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。本文对于时动边界上的热通量重构正问题的求解提出了人工边界的方法。在人工边界的基础上采用了位势理论方法求解此定解问题,并与前面已经给出的差分方法进行了比较。为了检验方法的可行性和两种方法的优劣,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 moving boundary. In this paper we use the artificial boundary to solve the moving boundary problem. Potential theory method is used to deal with this problem, compared with the method of difference already. Numerical results are given to support the proposed schemes and to give the compare of the two methods.

关 键 词：抛物方程 人工边界 位势理论 差分 数值模拟 

分 类 号：O175.26[理学—数学]