Application of Runge-Kutta Method in 3-D Coupled Netronics and Thermal-Hydraulics Transient Analysis

The coupled neutronics and thermal-hydraulics model is studied with the module coupling.Nodal Green’s Function Method（NGFM） based on the second boundary condition is used for solving neutronics module.The sub-channel code COBRA-Ⅳ is used for solving thermal-hydraulic module.Diagonally Implicit Runge-Kutta（DIRK） method is applied in the temporal discretization of coupled nonlinear equations.Automatic time step size control is achieved through Richardson Extrapolation or embedded lower order Runge-Kutta formulas.Hermite interpolation is used for continuous time variable solutions（dense output）.The solving procedure is based on block-iterative method,and the NCC code is developed.The numerical results show that the solution of NCC agrees well with reference solutions,and the DIRK（2,2）-E formula is more accurate and efficient than others in this paper.