Numerical Results for the Coupling of a Simple Neutronics Diffusion Model and a Simple Hydrodynamics Low Mach Number Model without Coupling Codes

• Published in: 2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) pp. 119 - 124
• Main Authors: Dellacherie, Stephane, Jamelot, Erell, Lafitte, Olivier, Mouhamad, Riyaz
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-09-2016
• Subjects: Couplings; Eigenvalues and eigenfunctions; Enthalpy; finite element analysis; Interpolation; Mathematical model; Neutrons; nuclear power generation; Numerical models; numerical simulation
• ISSN: 2470-881X
• DOI: 10.1109/SYNASC.2016.030

We obtain an analytic solution of a monodimensional stationary system coupling two simplified models, one solving the thermohydraulic equations, the other one solving the neutronic diffusion equation with one energy group (characterized by the diffusion coefficient, the absorption and the fission cross sections which are assumed to depend only on temperature). This analytic solution relies on the construction of two auxiliary functions. Realistic values of the cross sections (given at some values of the temperature) yield, by interpolation, approximate expressions for the cross sections. Projection of these functions on a 2d space using finite element method leads to a approximate simplified ODE, from which one deduces an approximation of the analytic solution using incomplete Jacobi elliptic integrals.