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

A Jacobian-Free Newton Krylov Two-Nodal Coarse Mesh Finite Difference algorithm based on Nodal Expansion Method (NEM_TNCMFD_JFNK) is successfully developed and proposed to solve the three-dimensional (3D) and multi-group reactor physics models. In the NEM_TNCMFD_JFNK method, the efficient JFNK method with the Modified Incomplete LU (MILU) preconditioner is integrated and applied into the discrete systems of the NEM-based two-node CMFD method by constructing the residual functions of only the nodal average fluxes and the eigenvalue. All the nonlinear corrective nodal coupling coefficients are updated on the basis of two-nodal NEM formulation including the discontinuity factor in every few newton steps. All the expansion coefficients and interface currents of the two-node NEM need not be chosen as the solution variables to evaluate the residual functions of the NEM_TNCMFD_JFNK method, therefore, the NEM_TNCMFD_JFNK method can greatly reduce the number of solution variables and the computational cost compared with the JFNK based on the conventional NEM. Finally the NEM_TNCMFD_JFNK code is developed and then analyzed by simulating the representative PWR MOX/UO₂ core benchmark, the popular NEACRP 3D core benchmark and the complicated full-core pin-by-pin homogenous core model. Numerical solutions show that the proposed NEM_TNCMFD_JFNK method with the MILU preconditioner has the good numerical accuracy and can obtain higher computational efficiency than the NEM-based two-node CMFD algorithm with the power method in the outer iteration and the Krylov method using the MILU preconditioner in the inner iteration, which indicates the NEM_TNCMFD_JFNK method can serve as a potential and efficient numerical tool for reactor neutron diffusion analysis module in the JFNK-based multiphysics coupling application.