Analysis of Hybrid MC/Deterministic Methods for Transport Problems Based on Low-Order Equations Discretized by Finite Volume Schemes

Abstract: This paper presents hybrid numerical techniques for solving the Boltzmann transport equation formulated by means of low-order equations for angular moments of the angular flux. The moment equations are derived by the projection operator approach. The projected equations are closed exactly using a high-order transport solution. The low-order equations of the hybrid methods are approximated with a finite volume scheme of the second-order accuracy. Functionals defining the closures in the discretized low-order equations are calculated by Monte Carlo techniques. In this study, we analyze effects of statistical noise and discretization error on the accuracy of the hybrid transport solution.