Upwind Finite Element Method for Solving Radiative Heat Transfer in Graded Index 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 problem, the upwind finite element methods based on streamline upwind (SU) and streamline upwind Petrov-Galerkin (SUPG) schemes are developed to solve multidimensional radiative heat transfer in semitransparent uniform and graded index media. Comparison between these two upwind schemes on the solution of RTE is carried out. The SUPG scheme is demonstrated to be better than the SU scheme as far as solution accuracy is concerned and have good accuracy in solution of radiative heat transfer in semitransparent graded index media.