A unified space-time fully-transversed general nodal expansion method for multidimensional and multigroup steady and transient nuclear reactor neutronics problems

摘要

A new unified space-time fully-transversed general nodal expansion method (STFT_GNEM) is developed to solve the multidimensional and multigroup steady and transient neutron diffusion problems by making full use of the transverse-integration technique and the respective advantages of the two popular nodal methods, the analytical nodal method (ANM) and the nodal expansion method (NEM). Specifically, the developed STFT_GNEM can easily obtain the ANM's local analytical solutions of all the transverse-integrated equations in the spatial coordinate directions based on the basis function expansion framework of the traditional NEM. The temporal operators are appropriately discretized using the transverse-integration procedure in the same way as the spatial operators and then the transverse integrated equations in the temporal direction are also analytically solved so that both the steady and transient nuclear reactor neutronics problems can be easily integrated into a unified nodal discretization formulation. Besides, the STFT_GNEM code can be easily developed from the existing NEM code. In this paper, the TWIGL reactor kinetics problem, the LRA super prompt-critical transient problem and the three dimensional transient LMW problem are analyzed to test the numerical properties of STFT_GNEM. Numerical results show that the STFT_GNEM code can track the reference solutions very well even on the coarse meshes and for large time-step sizes, which show the effectiveness and the potential of STFT_GNEM for steady and transient nuclear reactor neutronics problems. (C) 2019 Elsevier Ltd. All rights reserved.