二维稳态热传导问题中的辛方法  

Symplectic method in two dimensional thermal conduction under steady state

作　　者：徐新生[1] 周震寰[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,辽宁大连116024

出　　处：《热科学与技术》2006年第4期288-294,共7页Journal of Thermal Science and Technology

基　　金：国家自然科学基金资助项目(10272024)

摘　　要：通过引入哈密顿体系,提出一种求解二维稳态热传导问题的辛方法。将热传导问题归结为哈密顿体系下的本征值和本征解问题。利用辛本征解空间的完备性,建立一套封闭的求解问题方法。这种辛方法可直接求解各种边界条件问题,包括混合边界条件。研究结果表明,零本征值本征解描述了基本的均匀问题,而非零本征值本征解则显示着端部效应影响特点;数值算例给出了辛本征值和本征解的一些规律和具体例子,这些数值例子说明了由于非均匀端部的温度和热流影响的衰减规律;这种方法也为研究其他问题提供了一条路径。Hamiltonian s problem was reduced to yst fin symplectic eigensolutions, em was introduced f ding eigenvalues and a close method was or the thermal conduction under steady state. The eigensolutions. With the aid of the completeness of presented. The method can directly solve various problems of thermal conduction, including mixed boundaries. The result shows that zero-eigenvalue solutions describe basic problems, which are uniform and equivalent, and non-zero-eigenvalue solutions depict the effect of boundaries. Numerical examples show the decay character of the temperature and heat flux are caused by non uniform on boundaries. The symplectic method can provide a new idea for researching others problem.

关 键 词：温度场 热流密度 热传导 哈密顿体系 辛本征解 辛方法 

分 类 号：TK124[动力工程及工程热物理—工程热物理]