Finite element solution of the time-dependent SP3 equations using an implicit integration scheme

Boglárka Babcsány, Tamás Bartók, Dániel Péter Kis

29th Symposium of AER on VVER Reactor Physics and Reactor Safety (2019, Energoland, Mochovce NPP, Slovakia)
reactor dynamics and safety analysis


Today’s computational technology and its rapid development more and more enable the application of higher-order transport approximations and advanced numerical solution techniques even in reactor dynamic calculations. In view of this, 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 effort, it provides additional accuracy compared to diffusion theory. Besides – due to the fact that the multigroup 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 the developed algorithm, which applies Galerkin weighted residual method for spatial and implicit integration (the backward-difference method) for time discretization. Besides the developed solution algorithm, results of two-group kinetic SP3 calculations are also presented for various one-dimensional perturbations taking into account the delayed neutron precursor balance equations as well.

The nature of the SP3 equations detailed above and the flexibility of the applied finite element algorithm make the developed code named SPNDYN a good starting point for more realistic dynamic calculations in the future.

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