不连续温度场问题的间断Galerkin方法

A DISCONTINUOUS GALERKIN METHOD FOR DISCONTINUOUS TEMPERATURE FIELD PROBLEMS

针对不连续温度场问题建立了一种间断Galerkin有限元方法,该方法的主要特点是允许插值函数在单元边界上存在跳变.在建立有限元方程时,通过在单元边界上引入数值通量项和稳定性项来处理间断效应,并且数值通量可以直接由接触热阻的定义式导出.数值算例表明该方法可以很方便且准确地捕捉到结构内部由于接触热阻而引起的温度跳变,同时在局部高梯度温度场的模拟方面也比常规连续Galerkin有限元方法效率明显要高.该方法也为研究由接触热阻引起的温度场与应力场之间的耦合问题提供了一种新的数值模拟手段.

A discontinuous Galerkin（DG） finite element method for the discontinuous temperature field problems is presented.The DG method uses discontinuous interpolation functions on the element boundaries, and the discontinuous effect is considered by the penalty function techniques,in which the numerical flux and the stabilization term are adopted at the interface.By substituting the numerical flux at the imperfect contact interface with the definition of the thermal contact resistance,and eliminating the stabilization term,the present DG method can easily and accurately capture the temperature jump caused by thermal contact resistance. Compared with the continuous Galerkin method,the present DG method also has higher computational efficiency in capturing the peak value of the heat flux of the local high gradient temperature field.Numerical examples also show that the present DG method is a novel numerical method for solving the coupling problems between the temperature and stress field caused by thermal contact resistance.