A novel mathematical model for two-energy groups of the point kinetics reactor dynamics

作者：Aboanber Ahmed E^*; Nahla Abdallah A; Al Muhiameed Zeid I

来源：Progress in Nuclear Energy, 2014, 77: 160-166.

DOI：10.1016/j.pnucene.2014.06.016

• Neutron diffusion equations
• Two energy groups of the point kinetics equations
• Fundamental matrix
• Piecewise constant functions
• Multi-dimensional homogeneous reactors

The point kinetics equations for reactor dynamic systems are normally described and treated for one-energy group, which modeled as stiff coupled differential equations, and their solution by the conventional explicit methods will give a stable consistent result only for very small time steps. A novel analytical formulation is constructed and converged to high accuracy from the merger of the piecewise constant functions over a partition in time into the fundamental matrix for the two-energy group of the point kinetics equations. The resulting system of stiff linear and/or nonlinear differential equations for an arbitrary number of delayed neutrons is solved exactly over each time step. Through analytical inversion technique of the fundamental matrix and the stability of the method, we demonstrate its high accuracy for a variety of imposed reactivity insertions found in the literature for three dimensional homogeneous reactors. From knowledge of how the error term behaves the computational results indicate that the method is efficient and accurate for multi-dimensional homogeneous reactors.

• 出版日期2014-11