Spatial-angular spectral element method with discontinuous Galerkin schemes for radiative transfer in 2D irregular enclosures with obstacles based on unstructured spatial elements

In the article, we propose a spectral element method with discontinuous Galerkin schemes (SEDG) for solving radiative transfer problems in irregular enclosures with obstacles. The SEDG is used to discretize both angular and spatial domains. In the spatial domain, unstructured triangular elements with spectral collocation points are adopted to discretize the irregular enclosure with obstacles. In the angular direction, the structured quadrilateral elements with spectral collocation points are used, and a parallel computing strategy is employed to improve the computational efficiency. To smoothen the oscillations induced by the discontinuity in the spatial distribution of radiative intensity due to obstacle, an upwind approximate Reimann solver is developed to separate the incoming and outgoing information of radiative intensities on spatial element boundaries. Three examples are chosen to test the capability of the SEDG. Results demonstrate that the SEDG can flexibly provide hp convergence characteristics. Meanwhile, it can effectively minimize the non-physical oscillation in the spatial domain and angular direction, and can obtain the high angular resolution of radiative intensity.