High-order entropy-based closures for linear transport in slab geometry

Abstract

We compute, for the first time, high-order entropy-based ($M_N$) models for a linear transport equation on a one-dimensional, slab geometry. We simulate two test problems from the literature: the two-beam instability and the plane-source problem. In the former case we compute solutions for systems up to order $N=5$ ; in the latter, up to $N=15$. The most notable outcome of these results is the existence of shocks in the steady-state profiles of the two-beam instability for all odd values of $N$.