Upwind finite element method for solving radiative heat transfer in semitransparent media

Radiative transfer equation (RTE) in cartesian coordinates can be considered as a special kind of convective-diffusive equation with strong convection characteristics. For this convection dominated problem, standard finite element solutions often suffer from spurious oscillations. To avoid this, upwind finite element methods based on streamline upwinding (SU) and streamline upwinding petrov-galerkin (SUPG) schemes are developed to solve multidimensional radiative heat transfer in semitransparent media. Comparison between these two upwind schemes on the solution of RTE is carried out. It is shown that the SUPG scheme is better than the SU scheme as far as solution accuracy is concerned. Two test cases are taken as examples to verify the presented methods. The distributions of dimensionless temperature and net wall heat flux are calculated and compared to the results in references. By comparison, it is shown that the upwinding finite element methods developed have good accuracy in solution of radiative heat transfer in semitransparent media.