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

Abstract

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.