Analytic solutions and numerical method for a coupled thermo-neutronic problem

TL;DR

This paper presents an analytical and numerical approach to solving a simplified one-dimensional coupled thermo-neutronic problem in a nuclear reactor, achieving high accuracy and highlighting the impact of coefficient approximation.

Contribution

It introduces a combined analytical and numerical method for a coupled thermo-neutronic model, emphasizing the effects of coefficient approximation on results.

Findings

Both methods yield the same high-accuracy solution.

The benchmark quantity is sensitive to coefficient approximation.

Analytical representation uses incomplete elliptic integrals.

Abstract

We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this idealized nuclear core. These equations are coupled through the dependency of thecoefficients of the diffusion equation in terms of the enthalpy. We propose a numerical method treating globally the coupled problem for finding its unique solution.Simultaneously, we use incomplete elliptic integrals to represent analytically the density of neutrons and the enthalpy in the fluid. Both methods lead to the samesolution with high accuracy. However, another quantity, generally used as a benchmark for comparing results, depends considerably on the approximation used forthe coefficients of the diffusion equation.