Newton-Krylov method with nodal coupling coefficient to solve the coupled neutronics/thermal-hydraulics equations in PWR transient analysis

Abstract

This paper presents the solution to the neutronics equations coupled to a parallel channel model containing a 1D heat transfer model in PWR core transient calculation. Unlike traditional coupling techniques where the coupled field equations are solved separately, Newton-Krylov method is implemented to solve the coupled nonlinear field equations simultaneously. The related Jacobian of the nonlinear system is analytically derived based on the nonlinear residual functions and transferred into a compressed format which can be easily handled on a personal computer (PC). Since the Jacobian is explicitly constructed, it is directly passed to a GMRES solver with ILU preconditioning. A new solution strategy is proposed under the framework of Newton’s iteration, in which the nodal coupling coefficient (NCC) appeared in the neutronics equations is resolved in the Newton iteration level. The proposed method is studied by simulating all the six cases in the OECD NEACRP PWR rod ejection benchmark. Results indicate that that nonlinearity of NCC can be resolved in the Newton iteration level and can be further controlled by a user specified number, NNCC. Computational simulation also shows that the proposed method is capable to converge to a much tighter level with only a few iterations.