A multi-level nonlinear elimination-based JFNK method for multi-scale multi-physics coupling problem in pebble-bed HTR

Abstract

In the pebble-bed high-temperature gas-cooled reactor, various physical phenomena occur at different spatial scales and are coupled together tightly in a nonlinear manner. More specifically, the local temperature profiles inside the fuel sphere and TRISO particle, which are essential in reactor design and safety analysis, are coupled with the global physical fields, such as the pebble bed temperature, helium temperature, as well as the fission heat source. Therefore, the multi-physics calculation combined with multi-scale model should be employed to describe the reactor behavior. The computational efficiency is the critical issue for the numerical solution of such global and local coupled systems. Jacobian-free Newton Krylov (JFNK) algorithm is an excellent candidate for multi-physics coupling issues due to its high convergence rate and superior computational performance, but it doesn’t consider the physical features at different scales. In this work, a multi-level nonlinear elimination is proposed within the JFNK framework to deal with the multi-scale coupled system in high-temperature gas-cooled reactor. The numerous local multi-scale temperature variables, including the fuel sphere and TRISO particle temperatures, are eliminated efficiently based on the Schur complement factorization due to its well sparse matrix structure. As a result, the number of unknowns is significantly reduced and the computational performance is improved. A steady-state pebble-bed HTR model is used in this work, and the numerical results show that multi-level nonlinear elimination-based JFNK method has high computational efficiency and numerical robustness, whose performance is 4 ∼ 6 times higher than that of the original JFNK algorithm.