Unstructured Grids and the Multigroup Neutron Diffusion Equation

Abstract

The neutron diffusion equation is often used to perform core-level neutronic calculations. It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid. This work introduces the alternatives that unstructured grids can provide to aid the engineers to solve the neutron diffusion problem and gives a brief overview of the variety of possibilities they offer. It is by understanding the basic mathematics that lie beneath the equations that model real physical systems; better technical decisions can be made. It is in this spirit that this paper is written, giving a first introduction to the basic concepts which can be incorporated into core-level neutron flux computations. A simple two-dimensional homogeneous circular reactor is solved using a coarse unstructured grid in order to illustrate some basic differences between the finite volumes and the finite elements method. Also, the classic 2D IAEA PWR benchmark problem is solved for eighty combinations of symmetries, meshing algorithms, basic geometric entities, discretization schemes, and characteristic grid lengths, giving even more insight into the peculiarities that arise when solving the neutron diffusion equation using unstructured grids.