【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。更多还原

【Abstract】 Hamiltonian system was introduced for the thermal conduction under steady state. The problem was reduced to finding eigenvalues and eigensolutions.With the aid of the completeness of symplectic eigensolutions,a close method was 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.更多还原