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

Abstract

In Inertial Confinement 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 first 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 spherically symmetric model called P1′. 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 one-dimensional spherically symmetric case only. This scheme is well-balanced and satisfies the diffusion limit of the model. This scheme is validated by various numerical tests. We plan to extend this method to higher dimensions in a future work.