Solution of Radiative Transfer Equation for Plane-Parallel Medium Using a Discontinuous Galerkin Method and Adaptive Mesh Refinement

The discontinuous Galerkin (DG) finite element method (FEM) is employed to solve the radiative transfer equation (RTE) for plane-parallel problems, utilizing adaptive mesh refinement (AMR) techniques. In this approach, both spatial and angular directions are discretized using the DG method. This study specifically investigates the impact of AMR on the spatial variability of radiative intensity, aiming to enhance accuracy where it is most needed. To guide mesh refinement, the L-infinity norm is applied for error estimation. The space-angle DG method combined with AMR proves to be highly effective, providing accurate and efficient resolution of radiative heat transfer, particularly in regions that require more precise and accurate solutions.