Finite element solution of the time-dependent SP_3 equations using an implicit integration scheme

摘要

A coupled thermal-hydraulics and reactor physics code system is being developed at the Institute of Nuclear Techniques of the Budapest University of Technology and Economics based on a higher-order transport approximation, the simplified spherical harmonics theory. The advantage of this method is that with a small increase in computational demand, it provides additional accuracy compared to diffusion theory. Besides due to the fact that the multi-group SP3 and diffusion equations have a mathematically similar form - it requires minimal effort to implement an SP3 solution algorithm to an existing diffusion code. This paper focuses on an algorithm developed by the authors which applies Galerkin weighted residual method for spatial and theta method for time discretization. Results of two-group kinetic SP3 calculations performed with the SPNDYN code are also presented for various one-dimensional perturbations taking into account the delayed neutron precursor balance equations as well. The flexible nature of the SP3 equations makes the developed code a good starting point for more realistic dynamic calculations in the future.