Solução $ELTA_N$ para o Problema de Transporte com Fonte

A.V. Cardona; J.V.P de Oliveira

doi:10.5540/tema.2009.010.02.0125

Solução $ELTA_N$ para o Problema de Transporte com Fonte

A.V. Cardona, J.V.P de Oliveira

Abstract

Recentemente foi apresentada uma nova versão do método LTAN para resolver problemas de transporte lineares homogêneos em uma placa. Esta formulação foi denominada método $ELTA_N$ e é baseada na diagonalização de uma matriz N × N, em oposição a matriz (2N) × (2N) do método LTAN original. Neste trabalho estendemos essa formulação para resolver problemas de transporte não homogêneos. Simulações numéricas são apresentadas e os resultados são comparados aos resultados obtidos pelos métodos LTSN e LTAN.

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References

[1] L.B. Barichello, R.D.M. Garcia, C.E. Siewert, Particular solutions for the discrete ordinates method. Journal of Quantitative Spectroscopy and Radiative Transfer, 64 (2000), 219–266.

J.D. Brancher, M.T. Vilhena, C.F. Segatto, The LTSN Solution for radiative transfer problem without azimuthal symmetry with severe anisotropy, Journal of Quantitative Spectroscopy and Radiative Transfer, 62 (1999), 743–753.

A.V. Cardona, “Um Método Genérico de Solução Analítica para algumas Aproximações da Equação Linear de Transporte”, Tese de Doutorado, Engenharia Mecânica, UFRGS, Porto Alegre, RS, 1996.

A.V. Cardona, R.P. Pazos, M.T.M.B. Vilhena, The state-of-the-art of the LTAN method, in “Icone 12 - 12th International Conference on Nuclear Energy”, Proceeding of 12th International Conference on Nuclear Energy, Arlington, Virginia (EUA), ASME, 2004.

A.V. Cardona, R. Vasques, M.T.M.B. Vilhena, Uma nova versão do método LTAN, TEMA Tend. Mat. Apl. Comput., 5, No. 1, (2004), 49–54.

A.V. Cardona, M.T. Vilhena, A comparative study of analytical solutions for some one-dimensional transport equation approximations, Progress in Nuclear Energy, 33 (1998), 289–300.

A.V. Cardona, M.T.M.B. Vilhena, Analytical solution for the AN approximation, Annals of Nuclear Energy, 24 (1997), 495–505.

A.V. Cardona, M.T.M.B. Vilhena, Solução analítica da aproximação AN da equação de transporte linear com simetria planar, em “Anais do X Encontro de Física de Reatores e Termo-Hidráulica”, pp. 528–531, Águas de Lindóia, SP,

A.V. Cardona, M.T.M.B. Vilhena, J.V.P. de Oliveira, R. Vasques, The onedimensional LTAN solution in a Slab with high order of quadrature, in “Proceedings of 18th International Conference on Transport Theory”, pp. 260–264, Rio de Janeiro, Brazil, 2003.

R. Ciolini, G. Coppa, B. Montagnini, P. Ravetto, Simplified PN and AN methods in neutron transport, Progress in Nuclear Energy, 40 (2002), 237–264.

G. Coppa, P. Ravetto, An approximate method to study the one velocity neutron integral transport equation, Annals of Nuclear Energy, 9 (1982), 169–174.

G. Coppa, P. Ravetto, M. Sumini, The AN method in monokinetic transport theory: convergence and numerical approximations, Transport Theory and Statistical Physics, 10 (1981), 161–181.

G. Coppa, P. Ravetto, M. Sumini, Approximate solution to neutron transport equation with linear anisotropic scattering, Journal of Nuclear Science and Technology, 20 (1983), 822–831.

G. Coppa, P. Ravetto, M. Sumini, The AN Method and the spherical harmonics approximation in neutron transport theory, Annals of Nuclear Energy, 9 (1982), 435–437.

G. Coppa, P. Ravetto, M. Sumini, Numerical performance of the AN method and comparisons with SN calculations, Atomkernenergie Kerntechnik, 42 (1983), 107–110.

J. Duderstadt, W.R. Martin, “Transport Theory”, John Wiley & Sons, Inc., New York, 1979.

R.D.M. Garcia, C.E. Siewert, Benchmark Results in radiative transfer, Transport Theory and Statistical Physics, 14 (1985), 437–483.

G.A. Gonçalves, G. Orengo, M.T. Vilhena, C.O. Graça, LTSN Solution of the adjoint neutron transport equation with arbitrary source for high order of quadrature in a homogeneous Slab, Annals of Nuclear Energy, 29 (2002), 561–569.

G.A. Gonçalves, C.F. Segatto, M.T. Vilhena, The LTSN particular solution in a Slab for an srbitrary source and large order of quadrature, Journal of Quantitative Spectroscopy and Radiative Transfer, 66 (2000), 271–276.

W. Kaplan, “Ordinary Equations, Addison-Wesley: Reading”, Massachusetts, 1967.

J. Lenoble, “Standard Procedures to Compute Atmospheric Radiative Transfer in a Scattering Atmosphere”, NCAR, Boulder, 1977.

E.E. Lewis, F.W. Miller Jr., “Computational Methods of Neutron Transport”, American Nuclear Society, Illinois, 1993.

G.J. Marchuk, “Methods of Numerical Mathematics”, Springer-Verlag, New York, 1975.

R.P. Pazos, M. Thompson, M.T.M.B. Vilhena, Error bounds for spectral collocation method for the linear Boltzmann equation, International Journal of Computation and Numerical Analysis and Application, 1 (2002), 237–268.

R.P. Pazos, M.T.M.B. Vilhena, Convergence in transport theory, Applied Numerical Mathematics, 30 (1999), 79–92.

C.F. Segatto, M.T. Vilhena, The State-of-the-art of the LTSN Method, in “Proceedings of The International Conference on Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications”, Vol. 2, pp. 1618-1631, Madrid, Spain, 1999.

C.F. Segatto, M.T.M.B. Vilhena, M.G. Gomes, The one-dimensional LTSN solution in a Slab with high degree of quadrature, Annals of Nuclear Energy, 26 (1999), 924–925.

Z. Trzaska, An efficient algorithm for partial fraction expansion of the linear matrix pencil inverse, Journal of the Franklin Institute, 324 (1987), 465–477.

M.T. Vilhena, L.B. Barichello, A new analytical approach to solve the neutron transport equation, Kerntechnik, 56 (1991), 334–336.

M.T. Vilhena, L.B. Barichello, General approach to one-group one-dimensional

transport equation, Kerntechnik, 58 (1993), 182–184.

DOI: https://doi.org/10.5540/tema.2009.010.02.0125