Moment models for an axisymmetric inertial connement experiment and one dimensional numerical study

In Inertial Connement Fusion (ICF) experiments, radiation is well described by a kinetic model (radiative transfer equation). This model is usually too expensive to be used in numerical simulations of such phenomena. Hence, approximations are used. A common one is to use a moment model, in which the radiative transfer equation is replaced by its rst and second order (in velocity) moments, together with a closure assumption. In this article, we propose a closure for 2D and 3D geometries, which are extensions of a one-dimensional radially symmetric model called P'1. This model has proved to be very accurate in the study of ICF, which makes the models we propose promising in this respect. The closure is based on the fact that the model should, if possible, reproduce the exact solutions of radiative transfer equation in vacuum. We also design a numerical scheme for the radially symmetric case. This scheme is well-balanced and satises the diusion limit of the model. This scheme is validated by various numerical tests