非稳定导热问题有限元算法的守恒条件及一种守恒格式

本文对非稳定导热问题的有限元算法的能量守恒条件进行了讨论。认为有限元之解有时出现反常、振荡的原因是对问题时空域的离散化未能使相应格式满足能量守恒原理。依据文中的分析,提出了一种以单元边长做为集中热容阵权因子的守恒格式。验算表明,其稳定、可靠、精度较高。

CONSERVATION CONDITION AND A CONSERVATIVE SCHEME OF FINITE ELEMENT METHOD TO THE TRANSIENT HEAT CONDUTION PROBLEM

In this paper, energy conservation condition of finite element method (FEM) to the transient heat conduction problem have been discussed. It is believed that unreasonable temperature which sometimes appears in FEM computation is caused by the discretization of time and space domains which can not ensure the energy conservation principle.According to the analysis, a conservative FEM scheme is presented, in which side length of trianglar element is taken as weighting factor to the lumped capacitance matrix. The computation shows that the scheme is reliable, adaptable and have higher accuracy.