Ad hoc angular discretization of the radiative transfer equation

Y. Favennec (1) , T. Mathew (1) , Mohd Afeef Badri (1, 2) , Pierre Jolivet (3, 4) , Benoit Rousseau (1) , D. Lemonnier (5) , P.J. Coelho (6)

1 LTeN - Laboratoire de Thermique et d’Energie de Nantes
2 IRT Jules Verne - Institut de Recherche Technologique Jules Verne [Bouguenais]
3 IRIT-APO - Algorithmes Parallèles et Optimisation
4 CNRS - Centre National de la Recherche Scientifique
5 PPrime [Poitiers] - Institut Pprime [UPR 3346]
6 IDMEC - Instituto de Engenharia Mecânica [Lisboa]

Solving the radiative transfer equation 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 for increasing 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.

Domaines: Physique mathématique [math-ph]

Y. Favennec, T. Mathew, Mohd Afeef Badri, Pierre Jolivet, Benoit Rousseau, et al.. Ad hoc angular discretization of the radiative transfer equation. Journal of Quantitative Spectroscopy and Radiative Transfer, 2019, 225, pp.301-318. ⟨10.1016/j.jqsrt.2018.12.032⟩. ⟨hal-02333870⟩