Three-dimensional numerical model of neutron flux in hex-Z geometry. (English) Zbl 1206.82154

Hanuš, Milan; Berka, Tomáš; Brandner, Marek; Kužel, Roman; Matas, Aleš

Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 14. Proceedings of the seminar, Dolní Maxov, Czech Republic, June 1–6, 2008. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-55-4). 83-90 (2008).

The authors are interested in the stationary solution that characterizes neutron fluxes within the nuclear reactor core in an equilibrium state. It is presented a method for solving the equations of the neutron transport with discretized energetic dependence and angular dependence approximated by the diffusion theory. The set of steady-state neutron diffusion equations for \(G\) energy groups is given as follows:
\[ \nabla \cdot {\mathbf j}^g(\mathbf r)+\Sigma_r^g(\mathbf r)\phi^g(\mathbf r)= \sum^G_{\substack{ g'=1\\ g'\neq g}} \Sigma_s^{g'\to g}(\mathbf r)\phi^{g'}(\mathbf r)+\frac{\chi^g}{k_{\text{eff}}} \sum^G_{g'=1}\nu\Sigma_f^{g'}(\mathbf r)\phi^{g'}(\mathbf r) \]
according to the usual notation. The method effectively combines a whole-core coarse mesh calculation with a more detailed computation of fluxes based on the transverse integrated diffusion equations. The authors notes that by this approach, it achieves a good balance between accuracy and speed.
For the entire collection see [Zbl 1194.65013].

Reviewer: Dazmir Shulaia (Tbilisi)

MSC:

82D75

Nuclear reactor theory; neutron transport