Abstract: 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.

Key words: discontinuous Galerkin method, thermal contact resistance, high gradient, numerical flux, coupling nonlinearity