An improved semi-implicit direct kinetics method for transient analysis of nuclear reactors

  • Roozbeh VadiEmail author
  • Kamran Sepanloo


Semi-implicit direct kinetics (SIDK) is an innovative method for the temporal discretization of neutronic equations proposed by J. Banfield. The key approximation of the SIDK method is to substitute a time-averaged quantity for the fission source term in the delayed neutron differential equations. Hence, these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained, which leads to a significant reduction in computational cost. As the fission source is not known in a time step, the original study suggested using a constant quantity pertaining to the previous time step for this purpose, and a reduction in the size of the time step was proposed to lessen the imposed errors. However, this remedy notably diminishes the main advantage of the SIDK method. We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications, the mentioned drawbacks will be mitigated adequately. To test this idea, a novel multi-group, multi-dimensional diffusion code using the finite-volume method and a point-implicit solver is developed which works in both transient and steady states. In addition to the SIDK, two other kinetic methods, i.e., direct kinetics and higher-order backward discretization, are programmed into the diffusion code for comparison with the proposed model. The final code is tested at different conditions of two well-known transient benchmark problems. Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods, it reduces the total time required for computation by up to 24%.


Nuclear kinetics Semi-implicit direct kinetics Higher-order backward discretization Finite volume Point-implicit solver 



Semi-implicit direct kinetics


Finite-volume method


Higher-order backward discretization

Greek symbols


Heat-up conversion factor


Fission neutron fraction of a delayed neutron precursor group


Thermal feedback constant


Decay constant of a delayed neutron precursor group


Average number of neutrons released per fission


Neutron flux


Fission neutron energy spectrum


Macroscopic absorption cross section


Macroscopic fission cross section


Macroscopic scattering cross section from energy group g′ to g


Macroscopic removal cross section

List of symbols


Surface area vector of a face enclosing the target numerical cell


Concentration of delayed neutron precursor


Total number of numerical cells


Neutron diffusion coefficient


Total number of neutron energy groups


Effective multiplication factor


Total number of delayed neutron precursor groups


Total number of faces enclosing each cell


Power density









Subscripts and superscripts


Counter of faces enclosing each numerical cell


Counter of neutron energy group


Counter of numerical cells


Counter of time steps


Counter of delayed neutron precursor group


Counter of numerical iterations


Indicator of being an initial quantity


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Copyright information

© China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, Chinese Nuclear Society and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Nuclear Reactors and SafetyNuclear Science and Technology Research InstituteTehranIran

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