Hybrid Two-Level Transport Method with Solution Decomposition in Macro and Micro Components

Abstract

This paper presents a new hybrid MC/deterministic method for solving the one-group steady-state Boltzmann transport equation based on decomposition of solution in macro and micro components. The macro component captures the large-scale structure of the solution. It is represented by angular moments of the high-order transport solution. The $P_1$ approximation is applied to define the macro component. The first two angular moments are obtained as a solution of hybrid low-order moment equations with exact closures. The equation for the micro component is solved using a MC simulation. The hybrid two-level system of equations for macro and micro components is solved by fixed-point iteration scheme. Numerical results are presented to demonstrate variance reduction of stochastic numerical solution and improvement in computational efficiency.