ANN-MoC Method for Solving Unidimensional Neutral Particle Transport Problems
DOI:
https://doi.org/10.5540/03.2023.010.01.0019Palavras-chave:
Artificial Neural Networks, Method of Characteristics, Neutral Particle TransportResumo
Neutral particle transport problems are fundamental in the modeling of energy transfer by radiation (photons) and by neutrons with many important applications. In this work, the novel ANN-MoC method for solving unidimensional neutral particle transport problems is presented. Following the Method of Discrete Ordinates (DOM) and decoupling with a Source Iteration (SI) scheme, the proposed method applies Artificial Neural Networks (ANNs) together with the Method of Characteristics (MoC) to solve the transport problem. Once the SI scheme converges, the method gives an ANN that estimates the average flux of particles at any points in the computational domain. Details of the proposed method are given and results for two test cases are discussed. The achieve results show the potential of this novel approach for solving neutral particle transport problems.
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Referências
G.S. Abdoulaev and A.H. Hielscher. “Three-dimensional optical tomography with the equation of radiative transfer”. In: Journal of Electronic Imaging 12 (2003), pp. 594–601. doi:10.1117/1.1587730.
L.C. Evans. Partial Differential Equations. Graduate studies in mathematics. American Mathematical Society, 2010. isbn: 9780821849743.
M. Frank et al. “A comparison of approximate models for radiation in gas turbines”. In: Progress in Computational Fluid Dynamics 4 (2004), pp. 191–197. doi: 10 . 1504 / PCFD.2004.004087.
I. Goodfellow, Y. Bengio, and A. Courville. Deep Learning. London: Massachusetts Institute of Technology, 2014. isbn: 9780262035613.
S. Haykin. Neural Networks: A Comprehensive Foundation. Delhi: Pearson, 2005. isbn: 9780020327615.
A.H. Hielscher, R.E. Alcouffe, and R.L. Barbour. “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues”. In: Physics in Medicine & Biology 43 (1998), pp. 1285–1302. doi: 10 . 1088 / 0031 - 9155/43/5/017.
D.P. Kingma and J. Ba. Adam: A Method for Stochastic Optimization. 2017. arXiv: 1412.6980.
R.F. Knackfuss and L.B. Barichello. “On the temperature-jump problem in rarefied gas dynamics: the effect of the cercignani-lampis boundary conditon”. In: SIAM Journal of Applied Mathematics 66 (2006), pp. 2149–2186. doi: 10.1137/050643209.
E.W. Larsen et al. “Simplified P_N approximations to the equations of radiative heat transfer and applications”. In: Journal of computational Physics 183 (2002), pp. 652–675. doi: 10.1006/jcph.2002.7210.
E.E. Lewis and W.F. Miller. Computational Methods of Neutron Transport. New York: John Wiley & Sons, 1984. isbn: 9780894484698.
E. Meinköhn and S. Richling. “Radiative transfer with finite elements: II. Lyα line transfer in moving media”. In: Astronomy & Astrophysics 392 (2002), pp. 827–839. doi: 10.1051/ 0004-6361:20020951.
M.F. Modest. Radiative Heat Transfer. 3rd. Boston: Academic Press, 2013. isbn: 978-0123869449.
S. Richling et al. “Radiative transfer with finite elements: I. Basic method and tests”. In: Astronomy & Astrophysics 380 (2001), pp. 776–788. doi: 10.1051/0004-6361:20011411.
W.M. Stacey. Nuclear Reactor Physics. 2nd. Weinheim: Wiley, 2007. isbn: 9783527413669.
T. Tarvainen, M. Vauhkonen, and S.R. Arridge. “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation”. In: Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008), pp. 2767–2778. doi: 10.1016/j.jqsrt.2008.08.006.
R.F. Vargas, C.F. Segatto, and M.T. Vilhena. “Solution of the radiative heat transfer equation with internal energy sources in a slab by the LTSN method”. In: Journal of Quantitative Spectroscopy and Radiative Transfer 105.1 (2007), pp. 1–7. doi: 10.1016/j.jqsrt.2006.10.009.
R. Viskanta and M.P. Mengüç. “Radiation heat transfer in combustion systems”. In: Progress in Energy and Combustion Science 13 (1987), pp. 97–160. doi: 10.1016/0360-1285(87) 90008-6.
L.V. Wang and H. Wu. Biomedical Optics: Principles and Imaging. New Jersey: John Wiley & Sons, 2007. isbn: 9780471743040.
