Jacobian-free Newton Krylov two-node coarse mesh finite difference based on nodal expansion method for multiphysics coupled models

Abstract

A coupled Jacobian-Free Newton Krylov Two-Nodal Coarse Mesh Finite Difference algorithm based on Nodal Expansion Method (NEM_TNCMFD_JFNK) is successfully proposed and extended to solve the reactor core neutronics/thermal hydraulic (N/TH) coupled models in order to make full use of the respective high accuracy and efficiency advantages of the NEM, CMFD and JFNK methods. In the coupled NEM_TNCMFD_JFNK method, the efficient JFNK method is applied to the N/TH coupled nonlinear CMFD framework with three-dimensional (3D) neutron diffusion models, single-channel TH core models and fuel rod heat conduction models. Then the corrective nodal coupling coefficients in the nonlinear CMFD formulation are updated on the basis of the two-nodal high-order NEM method in every Newton steps to ensure the good accuracy of the CMFD method even on the coarse mesh size. In addition, the hybrid physics-based left preconditioners using the original Picard iterative strategies and algebraic-based right preconditioners with both the MILU method and the scaling matrix are developed to further improve the computational efficiency and convergence of the coupled NEM_TNCMFD _JFNK method. Numerical solutions of the representative NEACRP 3D core coupled benchmarks with different control rod positions and PWR 3D MOX/UO2 core coupled benchmarks with various burn-up and control banks show that the coupled NEM_TNCMFD _JFNK method can agree well with the reference and obtain the good or higher numerical efficiency compared with the NEM_TNCMFD method with Picard iteration, which demonstrates the potential and some advantages of the coupled NEM_TNCMFD_JFNK code for the reactor core multiphysics coupled models.