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

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 algebraicbased 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.