Multigroup Neutron Transport and Diffusion Computations

Abstract

The transport equation is introduced to describe a population of neutral particles such as neutrons or photons, in a close domain, under steady-state (i.e., stationary) conditions. Its derivation is based on the principle of particle conservation. The transport equation describes the statistical behavior of a large population of particles. The exact number of particles per unit volume is continuously varying with time, even at steady-state conditions. Under steady-state conditions, the number density of particles oscillates about an average value related to the solution of the steady-state transport equation. A solution of the transport equation is required in many fields of nuclear engineering, notably in reactor physics, in safety and criticality, and in radiation shielding and protection. We review legacy approaches for solving the steady-state transport equation, namely, the method of spherical harmonics, the collision probability method, the discrete ordinates method, and the method of characteristics. The full-core calculation consists of solving a simplified transport equation, either the diffusion equation or the simplified Pnequation.