Simulation for non-homogeneous transport equation by Nyström method

Authors

  • Luana Lazzari Universidade Federal do Rio Grande do Sul
  • Esequia Sauter Universidade Federal do Rio Grande do Sul
  • Fábio Souto De Azevedo Universidade Federal do Rio Grande do Sul

DOI:

https://doi.org/10.15392/bjrs.v8i3A.1507

Keywords:

transport equation, integral formulation, Nyström method

Abstract

In this work we solve numerically the one-dimensional transport equation with semi-reflective boundary conditions and non-homogeneous domain. The proposed methodology consists of applying the Nyström method in order to discretize the integral formulation of this problem which is an equation involving weakly singular integral operators. For this purpose, analytical and computational techniques were applied to deal with the singularities. The Nyström method is an integral method which approximates the integral operator by a numerical quadrature and turns the integral equation into a finite dimensional linear system. This formulation allows us to use any function to describe both scattering cross section and total cross section. The algorithm is implemented in C language with the use of routines of GNU scientific library and computational techniques for code optimization. The scalar flux was calculated for two numerical quadrature, namely Gauss-Legendre quadrature and Boole's rule. The numerical results were determined for transport problem with homogeneous and non-homogeneous domains. In order to validate the proposed method-ology, our numerical results were compared with those from the literature and presented with several correct significant digits.

Downloads

Download data is not yet available.

References

CHANDRASEKHAR, S. Radiative transfer, Dover Publications, Inc., Oxford University Press, London, 1950.

LEWIS, E. E.; MILLER, J. W. F. Computational Methods of Neutron Transport, Copyright, United States of America, 1984.

DALMOLIN, D.; DE AZEVEDO F. S.; SAUTER, E. Nyström method in transport equation, PROCEEDING OF INAC 2017 INTERNATIONAL NUCLEAR ATLANTIC CONFERENCE, Rio de Janeiro, Brazil, 2017.

DE AZEVEDO, F. S.; SAUTER, E.; KONZEN, P. H. A.; THOMPSON, M.; BARICHELLO, L. B. Integral formulation and numerical simulations for the neutron transport equation in X-Y geometry. Annals of Nuclear Energy, vol. 112, p. 735-747, 2018.

SAUTER, E.; DE AZEVEDO, F. S.; KONZEN, P. H. A. Nyström Method Applied to the Transport Equation in a Semi-Reflective Rectangle. Journal of Computational and Theoretical Transport, p. 2332-4325, 2019.

DELVES, L. M.; MOHAMED, J. L. Computational methods for integral equations, Cambridge, UK: Cambridge University Press, 1985.

NUNES, C. E. A.; BARROS, R. C. Aplicativo computacional para cálculos de blindagem com modelo de transporte Sn unidimensional e monoenergético, PROCEEDING OF INAC 2009 INTERNATIONAL NUCLEAR ATLANTIC CONFERENCE, Rio de Janeiro, Brazil, 2009.

GARCIA, R. D. M.; SIEWERT, C. E. Radiative transfer in finite inhomogeneous plane-parallel atmospheres. Journal of Quantitative Spectroscopy e Radiative Transfer, 2009.

Free Software Foundation, INC., 2009. GSL-GNU Scientific Library.

Downloads

Published

2021-02-09

How to Cite

Lazzari, L., Sauter, E., & De Azevedo, F. S. (2021). Simulation for non-homogeneous transport equation by Nyström method. Brazilian Journal of Radiation Sciences, 8(3A (Suppl.). https://doi.org/10.15392/bjrs.v8i3A.1507

Issue

Section

XXI Meeting on Nuclear Reactor Physics and Thermal Hydraulics (XXI ENFIR) and VI ENIN