龙格库塔方法在三维物理热工耦合瞬态分析中的应用

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

物理热工耦合采用模块化耦合方式,中子学空间求解采用第二类边界条件节块格林函数法(NGFM),热工水力求解采用COBRA-Ⅳ程序模块。耦合非线性方程的时间离散采用对角线隐式龙格库塔格式(DIRK),采用Richardson外推和嵌入低阶方法实现时步自适应,采用厄米插值得到连续时刻的解。采用块迭代方式求解离散方程开发NCC程序。数值验证结果表明,计算结果与参考结果符合较好,DIRK(2,2)-E格式是本文所采用的格式中精度、效率较高的。

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 contirluous 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.