Spectral element method for solving radiative heat transfer in semi-transparent media

Radiative transfer equation (RTE) in Cartesian coordinates can be considered as a special kind of convective-diffusive equation and is convection dominated. Numerical solution of the convection dominated problem often suffers from spurious oscillations. The spectral element method based on streamline upwind Petrov-Galerkin (SUPG) stabilization scheme was developed to solve multidimensional radiative heat transfer in semi-transparent media. Three test cases were taken as examples to verify the performance of the SUPG spectral element method for solving multi-dimensional radiative heat transfer in semi-transparent media. The SUPG spectral element method effectively diminished the spurious oscillations as compared with the Galerkin spectral element method. The distributions of radiative intensity and net wall heat flux were calculated and compared with the analytical results and data in references. By comparison, it was shown that the SUPG spectral element method developed in this paper had good accuracy in solving radiative heat transfer in semi-transparent media.