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Cromianski S, Rui K, Barichello L. A study on boundary fluxes approximation in explicit nodal formulations for the solution of the two-dimensional neutron transport equation. PROGRESS IN NUCLEAR ENERGY 2019. [DOI: 10.1016/j.pnucene.2018.09.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Picoloto C, da Cunha R, Barros R, Barichello L. An analytical approach for solving a nodal formulation of two-dimensional fixed-source neutron transport problems with linearly anisotropic scattering. PROGRESS IN NUCLEAR ENERGY 2017. [DOI: 10.1016/j.pnucene.2017.03.017] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Closed-form solutions for nodal formulations of two dimensional transport problems in heterogeneous media. ANN NUCL ENERGY 2015. [DOI: 10.1016/j.anucene.2015.04.013] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Barichello LB, da Cunha RD, Picoloto CB, Tres A. An analytical approach for a nodal formulation of a two-dimensional fixed-source neutron transport problem in heterogeneous medium. KERNTECHNIK 2015. [DOI: 10.3139/124.110468] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
Abstract
A nodal formulation of a fixed-source two-dimensional neutron transport problem, in Cartesian geometry, defined in a heterogeneous medium, is solved by an analytical approach. Explicit expressions, in terms of the spatial variables, are derived for averaged fluxes in each region in which the domain is subdivided. The procedure is an extension of an analytical discrete ordinates method, the ADO method, for the solution of the two-dimensional homogeneous medium case. The scheme is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric quadrature scheme. As usual for nodal schemes, relations between the averaged fluxes and the unknown angular fluxes at the contours are introduced as auxiliary equations. Numerical results are in agreement with results available in the literature.
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Affiliation(s)
- L. B. Barichello
- Instituto de Matemática , Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500 – Campus do Vale, 91509-900 Porto Alegre, RS , Brasil. E-mail:
| | - R. D. da Cunha
- Instituto de Matemática , Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500 – Campus do Vale, 91509-900 Porto Alegre, RS , Brasil. E-mail:
| | - C. B. Picoloto
- Programa de Pós-Graduação em Engenharia Mecânica , Universidade Federal do Rio Grande do Sul, Sarmento Leite, 425, 90050-170 Porto Alegre, RS , Brasil. E-mail:
| | - A. Tres
- Programa de Pós-Graduação em Matemática Aplicada , Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500 – Campus do Vale, 91509-900 Porto Alegre, RS , Brasil. E-mail:
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