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

Abstract

We obtain an analytic solution of a monodimensionalstationary system coupling two simplified models, one solving the thermohydraulic equations, the other onesolving the neutronic diffusion equation with one energygroup (characterized by the diffusion coefficient, the absorptionand the fission cross sections which are assumed to dependonly on temperature). This analytic solution relies on theconstruction of two auxiliary functions. Realistic values of thecross 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 elementmethod leads to a approximate simplified ODE, from whichone deduces an approximation of the analytic solution usingincomplete Jacobi elliptic integrals.