One-dimensional Riemann solvers and the maximum entropy closure

Abstract

The maximum entropy closure for the two-moment approximation of the neutron transport equation is presented. We use a robust Roe-type Riemann solver to solve the resulting moment equations. We also present three boundary conditions to use with this method. The ghost cell method effectively implements the Mark boundary condition by placing phantom cells just outside the physical system. This method is extremely simple to implement and gives reasonable results. The boundary Eddington factor method implements the Marshak boundary condition. While it yields good results at boundaries with incoming neutrons, it does not do so well at vacuum boundaries. The partial numerical flux method is an extension of the Marshak boundary condition, allowing us to specify extra angular information about the incoming neutron distribution. The neutron flux calculations with this method are generally the best out of the three boundary conditions presented here. Several simple steady-state and time-dependent problems illustrate the qualities, both good and bad, of the maximum entropy closure.