Stochastic-deterministic response matrix method for reactor transients

Abstract

Presented is a stochastic-deterministic, response matrix method for transient analyses of nuclear systems. The method is based on the response matrix formalism, which describes a system by a set of response functions. We propose an approach in which these response functions are computed during a set of Monte Carlo criticality calculations and are later used to formulate a deterministic set of equations for solving a space-time dependent problem. Application of the response matrix formalism results in a set of loosely connected equations, which leads to a favourable linear scaling of the problem. The method offers a simplified approach compared to previously proposed response matrix methods by avoiding phase-space expansions in sets of basis functions. We describe the method starting with the fundamental neutron transport considerations, provide a demonstration on two absorber movement transients in a 3 × 3 assembly PWR mini-core geometry, and compare the solutions against time-dependent Monte Carlo simulations.