An analytic and symbolic analysis of a coupled thermo-neutronic problem

Francois Dubois (1, 2, 3) , Olivier Lafitte (4, 2)

1 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés
2 CRM - Centre de Recherches Mathématiques [Montréal]
3 LMO - Laboratoire de Mathématiques d'Orsay
4 LAGA - Laboratoire Analyse, Géométrie et Applications

In this paper, we seek analytical approximate solutions of a problem coupling the neutronics equation and the thermal equation (using incomplete Elliptic integrals), and we compare these analytical approximate solutions to a numerical method for the coupled problem, using a Crank-Nicolson scheme for the thermal equation and an generalized eigenvalue problem for the neutronics equation. Both the approximate analytical methods and the numerical method amount to finding the multiplication factor keff (k−1eff is the generalized eigenvalue) as the unique solution of an equation. All methods yield values of keff close to each other with a difference of magnitude 10−7, which is much better than what is generally needed in neutronics.

Keywords: Ordinary differential equation; analytic special functions; Crank-Nicolson numerical scheme; Couplings; Scientific computing; Integral equations; Eigenvalues and eigenfunctions; Thermal analysis

Domains: Mathematics [math]

Francois Dubois, Olivier Lafitte. An analytic and symbolic analysis of a coupled thermo-neutronic problem. 2021 23rd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), Dec 2021, Timisoara, Romania. pp.61-65, ⟨10.1109/SYNASC54541.2021.00022⟩. ⟨hal-03659886⟩