The Nodal LTSN Solution in a Rectangular Domain: A New Method to Determine the Outgoing Angular Flux at the Boundary

  • Aline R. Parigi
  • Cynthia F. Segatto
  • Bardo E. J. BodmannEmail author


In the present contribution we discuss the neutron nodal SN equation in a rectangular domain. The nodal method consists in transverse integration of the SN equation and results in coupled one-dimensional SN equations with unknown angular flux at the border. In the literature, the outgoing angular flux is considered a constant or exponential decreasing function, where the latter is used in this work. It is noteworthy that solutions found with these boundary conditions present unphysical results, i.e. negative angular fluxes in the border region, whereas the scalar flux is semi-positive definite. To overcome these shortcomings a new approach is proposed. The rectangular domain is covered by a finite discrete set of narrow rectangular sub-domains, so that in each rectangle the solution may be approximated by the one from a one-dimensional problem. Upon applying the LTSN method combined with the DNI technique, i.e. interpolating the directions of the two-dimensional problem by means of one-dimensional directions, one obtains the angular flux at the border from the known one-dimensional LTSN solution for any desired point. Numerical simulations and comparisons with results found in the literature are presented.


  1. [ChEtAl00]
    Chalhoub, E. S., and Garcia, R. D. M.: In The equivalence between two techniques of angular interpolation for the discrete-ordinates method, Journal of Quantitative Spectroscopy & Radiative Transfer, 64, 517–535 (2000).Google Scholar
  2. [HaEtAl02]
    Hauser, E. B., Panta Pazos, R., Barros, R.C., and Vilhena, M. T.: In Solution and study of Nodal Neutron Transport Equation applying the LTS N DiagExp Method, Proceedings of the 18th International Conference on Transport Theory, Rio de Janeiro, Brazil, 303–307 (2002).Google Scholar
  3. [LeEtAl93]
    Lewis, E., and Mille, W.: In Computational Methods of Neutron Transport, John Wiley and Sons, New York (1993).Google Scholar
  4. [SeEtAl99b]
    Segatto, C. F., Vilhena, M. T., and Gomes, M.: In The One-Dimensional LTSN Solution in a Slab with High Degree of Quadrature, Annals of Nuclear Energy, 26, 925–934 (1999b).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Aline R. Parigi
    • 1
  • Cynthia F. Segatto
    • 2
  • Bardo E. J. Bodmann
    • 2
    Email author
  1. 1.Instituto Federal FarroupilhaSanta MariaBrazil
  2. 2.Universidade Federal do Rio Grande do SulPorto AlegreBrazil

Personalised recommendations