Discontinuous finite element solutions for coupled radiation-conduction heat transfer in irregular media

The discontinuous finite element method (DFEM) is used to investigate the coupled radiation-conduction heat transfer in an irregular medium, and the highly accurate solutions for several typical media are numerically obtained. Comparing with the traditional continuous finite element method, the computational domain in the DFEM application is discretized into unstructured meshes that are assumed to be separated from each other. The shape function construction, field variable approximation, and numerical solutions are obtained for every single element. The continuity of the computational domain is maintained by modeling a numerical flux with the up-winding scheme. Thus the DFEM has the salient feature of geometry flexibility and simultaneously supports locally conservative solutions. The DFEM discretization for the radiative transfer equation and the energy diffusion equation are first presented, and the accuracies of the DFEM for coupled radiation-conduction heat transfer problems are verified. Combined radiation-conduction heat transfer problems in several irregular media are afterward solved, and the highly accurate DFEM solutions are presented.