Ad hoc angular discretization of the radiative transfer equation

Abstract

Solving the radiative transfer equation (RTE) with the finite element method requires both angular and spatial discretizations. We develop a novel algorithm of angular mesh discretization based on a posteriori calculations. The obtained angular discretizations are optimized in such a way that they suit the particular physics under consideration. Such ad hoc angular discretizations are implemented to increase the finite element solution efficiency. Using comparative numerical tests based on the solution accuracy, the solutions provided by the obtained ad hoc discretizations are proven to be better than the ones provided by the standard uniform angular discretizations. The algorithm is drafted in such a way that it could be easily implemented using pre-existing open-source mathematical libraries. This paper is an extended version of a paper presented at the CTRPM-VI conference [1]. As an extension to the two-dimensional version presented at the conference, a three-dimensional adaptive ad hoc angular discretization of the RTE is addressed here.