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.
While more than a decade ago reactor and thermal hydraulic calculations were tedious and often needed a lot of approximations and simplifications that forced the designers to take a very conservative approach, computational resources available nowadays allow engineers to cope with increasingly complex problems in a reasonable time. The use of best-estimate calculations provides tools to justify convenient engineering margins, reduces costs, and maximises economic benefits. In this direction, a suite of coupled best-estimate specific calculation codes was developed to analyse the behaviour of the Atucha II nuclear power plant in Argentina. The developed tool includes three-dimensional spatial neutron kinetics, a channel-level model of the core thermal hydraulics with subcooled boiling correlations, a one-dimensional model of the primary and secondary circuits including pumps, steam generators, heat exchangers, and the turbine with all their associated control loops, and a complete simulation of the reactor control, limitation, and protection system working in closed-loop conditions as a faithful representation of the real power plant. In the present paper, a description of the coupling scheme between the codes involved is given, and some examples of their application to Atucha II are shown.
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