A study on boundary fluxes approximation in explicit nodal formulations for the solution of the two-dimensional neutron transport equation

• Published in: Progress in nuclear energy (New series) Vol. 110; pp. 354 - 363
• Main Authors: Cromianski, S.R., Rui, K., Barichello, L.B.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.01.2019; Elsevier BV
• Subjects: Auxiliary equations; Discrete element method; Discrete ordinates; Exponential functions; Fixed-source problems; Fluxes; Formulations; Homogeneous and heterogeneous medium; Mathematical analysis; Neutrons; Nodal methods; Nuclear energy; Two dimensional analysis; Two-dimensional transport; Discrete ordinates; Fixed-source problems; Homogeneous and heterogeneous medium; Nodal methods; Auxiliary equations; Two-dimensional transport
• ISSN: 0149-1970; 1878-4224
• DOI: 10.1016/j.pnucene.2018.09.006

When deriving nodal methods, the known process of transverse integration introduces additional unknowns to the problem, related to the leakage terms. Additional auxiliary equations must be proposed in order to close the system and to allow its solution. In this work, a study on approximations to those unknowns, fluxes on the contours of the nodes, is carried out. In particular, two-dimensional fixed-source problems are analyzed. Therefore, three alternative proposals of approximations are considered: constant, linear and exponential functions. Such approaches are employed along with of the ADO method, which is used to solve the one-dimensional transversely integrated equations. Numerical results for section averaged scalar fluxes are presented and compared with other nodal schemes, showing some differences among the various approximations, mainly for coarse meshes, although satisfactory comparisons are achieved in the source region.