Efficient simultaneous solution of multi-physics multi-scale nonlinear coupled system in HTR reactor based on nonlinear elimination method

Pebble bed HTR reactor core is a globally coupled system involving neutronics and thermal-hydraulic field. At the same time, the locally coupled relations exist in fuel sphere temperature, local neutron flux and pebble bed temperature. What's more, several types of fuel spheres with different burnup and fission power must be treated separately. Due to the essential difference between local and global coupling properties, the method, named nonlinear elimination (NlEm), is developed in this paper to solve the multi-physics/multi-scale system of HTR in a tightly coupled, two-level nonlinear form. In the NlEm framework, the local coupled variables and the global coupled variables are treated separately at two different levels to enhance the computational efficiency. For comparison, the Jacobian-free Newton Krylov (JFNK) method and the Picard method are utilized to solve the multi-physics/multi-scale system respectively. The numerical results reveal that the computational efficiency of NlEm is 6.7 times higher than that of Picard method and 3.5 times higher than that of JFNK method for five transient cases of a two-dimension simplified reactor model. And with the increase of the computational scale and time step size, the speedup ratio of NlEm is further raised.