Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation

Rakotondravanona Jean Eric; Raboanary Roland

doi:doi:10.11648/j.wjap.20180302.12

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Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation

Rakotondravanona Jean Eric, Raboanary Roland

Published in World Journal of Applied Physics (Volume 3, Issue 2)

Received: 19 May 2018 Accepted: 6 June 2018 Published: 7 July 2018

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Abstract

In this paper, an approach of determining analytical solutions of the mono-kinetic multiregion neutron diffusion equation from two-dimensional Cartesian geometry is presented. The technical approach is based on the Lie symmetry group for partial differential equation. The local symmetry groups to the one-parameter transformation are obtained. The invariant solutions spanned of an expansion of neutron fluxes with respect to the space, time and material regions are reported.

Published in	World Journal of Applied Physics (Volume 3, Issue 2)
DOI	10.11648/j.wjap.20180302.12
Page(s)	25-33
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Multiregion Neutron Diffusion Equation, Symmetry Groups, Invariant Solutions

References

[1]	Bell, George I. and Glasstone Samuel: “Nuclear Reactor Theory”, Van Nostrand Reinhold, 1970.
[2]	James J. Duderstadt, Louis J. Hamilton: “Nuclear Reactor Analysis”, Department of Nuclear Engineering, University of Michigan, 1976.
[3]	R. A. Shober: “A Nodal Method For solving Transient Few-group Neutron Diffusion Equation”, Applied Physics Division, Argonne National Laboratory, pp 11-17, June 1978.
[4]	Alain Hebert: “Multigroup Neutron Tranport and Diffusion Computations”, Handbook of Nuclear Engineering, Vol. 2, Editor: Dan Gabriel Cacuci, pp 753-911, 2010.
[5]	Joe. W. Durkee Jr: “Exact solution to the time-dependent one-speed multiregion neutron diffusion equation”, Progress in Nuclear Energy, Volume 3, No 3, pp 191-222, 1994.
[6]	Ovsyannikov L. V.: “Group Analysis of Differential Equations”, New York Academic Press, 1982.
[7]	Peter J. Olver: “Applications of Lie Groups to Differential Equations”, Springer - Verlag, New York, Grad. Texts in Math. 107, 1986.
[8]	Nail H. Ibragimov: “CRC Handbook of Lie Group Analysis of Differential Equations”, Vol. 1: Symmetries, Exact Solutions and Conservation Laws, CRC Press, Boca Raton, 1994.
[9]	Brian Christensen: “Three-dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method”, Risø National Laboratory, DK-4000 Roskilde, Denmark, 1985.
[10]	E. Z. Muller and Z. J. Weiss: “Benchmarking with the multi-group diffusion high-order response matrix method”, Annals of Nuclear Energy, vol. 18, no. 9, pp. 535–544, 1991.
[11]	Ivan Tsyfra and Tomasz Czyżycki: “Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media”, Hindawi Publishing Corporation, Volume 2014, Article ID 724238, 17 June 2014.
[12]	Seyed Abolfazl Hosseini: “Sensitivity Analysis of the Galerkin Finite Element Method Neutron Diffusion Solver to the Shape of the Elements”, Nuclear Engineering and Technology 49 (2017), 29-42, 8 August 2016.
[13]	Seyed Abolfazl Hosseini and Farahnaz Saadatian-Derakhshande: “Galerkin and Generalized Least Squares finite element: A comparative study for multi-group diffusion solvers”, Progress in Nuclear Energy 85, 473-490, 20 July 2015.
[14]	Sukanta Nayak and S. Chakraverty: “Numerical Solution of two group uncertain neutron diffusion equation for multiregion reactor”, Third International Conference on Advances in Control and Optimization of Dynamical Systems, Kanpur, India, March 13-15, 2014.

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APA Style

Rakotondravanona Jean Eric, Raboanary Roland. (2018). Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation. World Journal of Applied Physics, 3(2), 25-33. https://doi.org/10.11648/j.wjap.20180302.12

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ACS Style

Rakotondravanona Jean Eric; Raboanary Roland. Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation. World J. Appl. Phys. 2018, 3(2), 25-33. doi: 10.11648/j.wjap.20180302.12

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AMA Style

Rakotondravanona Jean Eric, Raboanary Roland. Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation. World J Appl Phys. 2018;3(2):25-33. doi: 10.11648/j.wjap.20180302.12

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@article{10.11648/j.wjap.20180302.12,
  author = {Rakotondravanona Jean Eric and Raboanary Roland},
  title = {Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation},
  journal = {World Journal of Applied Physics},
  volume = {3},
  number = {2},
  pages = {25-33},
  doi = {10.11648/j.wjap.20180302.12},
  url = {https://doi.org/10.11648/j.wjap.20180302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wjap.20180302.12},
  abstract = {In this paper, an approach of determining analytical solutions of the mono-kinetic multiregion neutron diffusion equation from two-dimensional Cartesian geometry is presented. The technical approach is based on the Lie symmetry group for partial differential equation. The local symmetry groups to the one-parameter transformation are obtained. The invariant solutions spanned of an expansion of neutron fluxes with respect to the space, time and material regions are reported.},
 year = {2018}
}

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TY  - JOUR
T1  - Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation
AU  - Rakotondravanona Jean Eric
AU  - Raboanary Roland
Y1  - 2018/07/07
PY  - 2018
N1  - https://doi.org/10.11648/j.wjap.20180302.12
DO  - 10.11648/j.wjap.20180302.12
T2  - World Journal of Applied Physics
JF  - World Journal of Applied Physics
JO  - World Journal of Applied Physics
SP  - 25
EP  - 33
PB  - Science Publishing Group
SN  - 2637-6008
UR  - https://doi.org/10.11648/j.wjap.20180302.12
AB  - In this paper, an approach of determining analytical solutions of the mono-kinetic multiregion neutron diffusion equation from two-dimensional Cartesian geometry is presented. The technical approach is based on the Lie symmetry group for partial differential equation. The local symmetry groups to the one-parameter transformation are obtained. The invariant solutions spanned of an expansion of neutron fluxes with respect to the space, time and material regions are reported.
VL  - 3
IS  - 2
ER  -

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Author Information

Rakotondravanona Jean Eric

Department of Physics & Applications, University of Antananarivo, Antananarivo, Madagascar
Raboanary Roland

Department of Physics & Applications, University of Antananarivo, Antananarivo, Madagascar

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APA Style

Rakotondravanona Jean Eric, Raboanary Roland. (2018). Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation. World Journal of Applied Physics, 3(2), 25-33. https://doi.org/10.11648/j.wjap.20180302.12

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ACS Style

Rakotondravanona Jean Eric; Raboanary Roland. Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation. World J. Appl. Phys. 2018, 3(2), 25-33. doi: 10.11648/j.wjap.20180302.12

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AMA Style

Rakotondravanona Jean Eric, Raboanary Roland. Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation. World J Appl Phys. 2018;3(2):25-33. doi: 10.11648/j.wjap.20180302.12

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@article{10.11648/j.wjap.20180302.12,
  author = {Rakotondravanona Jean Eric and Raboanary Roland},
  title = {Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation},
  journal = {World Journal of Applied Physics},
  volume = {3},
  number = {2},
  pages = {25-33},
  doi = {10.11648/j.wjap.20180302.12},
  url = {https://doi.org/10.11648/j.wjap.20180302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wjap.20180302.12},
  abstract = {In this paper, an approach of determining analytical solutions of the mono-kinetic multiregion neutron diffusion equation from two-dimensional Cartesian geometry is presented. The technical approach is based on the Lie symmetry group for partial differential equation. The local symmetry groups to the one-parameter transformation are obtained. The invariant solutions spanned of an expansion of neutron fluxes with respect to the space, time and material regions are reported.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Lie symmetry Analysis and Invariant Solutions for Multiregion Neutron Diffusion Equation
AU  - Rakotondravanona Jean Eric
AU  - Raboanary Roland
Y1  - 2018/07/07
PY  - 2018
N1  - https://doi.org/10.11648/j.wjap.20180302.12
DO  - 10.11648/j.wjap.20180302.12
T2  - World Journal of Applied Physics
JF  - World Journal of Applied Physics
JO  - World Journal of Applied Physics
SP  - 25
EP  - 33
PB  - Science Publishing Group
SN  - 2637-6008
UR  - https://doi.org/10.11648/j.wjap.20180302.12
AB  - In this paper, an approach of determining analytical solutions of the mono-kinetic multiregion neutron diffusion equation from two-dimensional Cartesian geometry is presented. The technical approach is based on the Lie symmetry group for partial differential equation. The local symmetry groups to the one-parameter transformation are obtained. The invariant solutions spanned of an expansion of neutron fluxes with respect to the space, time and material regions are reported.
VL  - 3
IS  - 2
ER  -

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