Numerical optimization of a multiphysics calculation scheme based on partial convergence

Abstract

This paper deals with the numerical optimization of a multiphysics calculation scheme. The purpose of this tool is the fine-scale neutronic and thermal-hydraulic modelling of Pressurized Water Reactors (PWRs), under steady-state nominal conditions and fission products equilibrium concentrations. The neutronic model follows a two-steps approach with pin-cell homogenization. The considered coupling scheme includes the neutronic core model, the subchannel thermal-hydraulic and heat conduction one and the isotopic depletion one. From the numerical standpoint, this problem is a large system of non-linear equations. For its resolution, two standard numerical methods are considered, the damped fixed-point method and the Anderson acceleration. In particular, this work focuses on the application of the partial-convergences within these methods. The partial-convergence technique deals with the research of a progressive internal convergence of the considered neutronic and thermal-hydraulic solvers. Within this approach, the degree of convergence is controlled either by limiting the number of single-solver iterations or by adjusting the required precisions on the respective key variables. To realise a large number of simulations in an affordable time, the chosen case study is a mini-core (5 × 5 PWR fuel assemblies plus reflector). The application of the partial-convergences to the fixed-point algorithm is rather common in the industry, but few systematic studies have been published. The impact of limiting both the neutronic and the thermal-hydraulic iterations is deeply analysed. In this context, the partial-convergences allow to strongly increase the robustness and the efficiency of the fixed-point method. For what concerns the application of this technique to the Anderson algorithm, a new strategy is proposed and preliminary tests show promising results.