Coupling methods for HTR-PM primary circuit

The purpose of this paper is to analyze coupling methods for High-Temperature Gas-Cooled Reactor-Pebble bed Module (HTR-PM) primary circuit, including reactor core, steam generator, and other components. Each component has individual characteristics and is simulated by an independent code package. A feasible way to integrate these independent codes is by using Picard iteration. In practice, the primary circuit is divided into multiple parts based on physical fields or spatial domains. Another coupling method is Jacobian-free Newton-Krylov (JFNK), which is frequently applied for the simulation of coupled multi-physics systems due to its efficiency and capability for large-scale nonlinear problems. To demonstrate the efficiency of coupling method for tightly coupled primary circuit systems, several Picard and JFNK methods were compared consistently in this paper, where all the models, equations and codes for each method are the same. Especially for neutronics, we use the same additional equation for JFNK as the outer iteration step in power iteration. Results show that the equations in the reactor core and outside the reactor core should be solved simultaneously in Picard iteration, otherwise additional thermal-hydraulics iterations are necessary. JFNK methods have shown better convergence behavior than Picard iteration, especially for computational efficiency. Since the nonlinear residual is evaluated directly from nonlinear equation set without iteration, linear preconditioned JFNK has shown efficient convergence, which is recommended by the authors as the first choice for HTR-PM primary circuit if the linear preconditioned JFNK is applicable and the well-performing preconditioner is available. However, for utilizing physical iteration processes, nonlinear preconditioned JFNK is a practical choice when integrating legacy codes.