An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case

Okey Oseloka Onyejekwe

doi:doi:10.11648/j.ijfmts.20170301.11

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An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case

Okey Oseloka Onyejekwe

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 3, Issue 1)

Received: 11 December 2016 Accepted: 26 December 2016 Published: 24 January 2017

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Abstract

To further improve on the competitiveness of the boundary element method (BEM), a hybrid version of it is used for a numerical solution of two dimensional nonlinear coupled viscous Burger’s equation. Adopting this approach to a discretized 2D spatial domain, the resulting integral equations arising from the singular integral theory are applied locally to each of the elements. The resulting nonlinear discrete equations are finally solved by the Picard iteration algorithm. The simulation results obtained, not only concur with analytical solutions, but also display high accuracy and are in agreement with those available in literature.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 3, Issue 1)
DOI	10.11648/j.ijfmts.20170301.11
Page(s)	1-15
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

Two Dimensional, Coupled Nonlinear Burger’S Equation, Hybrid Boundary Element Method, Integral Equation, Singular Integral Theory, Discretization

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Okey Oseloka Onyejekwe. (2017). An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case. International Journal of Fluid Mechanics & Thermal Sciences, 3(1), 1-15. https://doi.org/10.11648/j.ijfmts.20170301.11

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Okey Oseloka Onyejekwe. An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case. Int. J. Fluid Mech. Therm. Sci. 2017, 3(1), 1-15. doi: 10.11648/j.ijfmts.20170301.11

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AMA Style

Okey Oseloka Onyejekwe. An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case. Int J Fluid Mech Therm Sci. 2017;3(1):1-15. doi: 10.11648/j.ijfmts.20170301.11

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@article{10.11648/j.ijfmts.20170301.11,
  author = {Okey Oseloka Onyejekwe},
  title = {An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {3},
  number = {1},
  pages = {1-15},
  doi = {10.11648/j.ijfmts.20170301.11},
  url = {https://doi.org/10.11648/j.ijfmts.20170301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20170301.11},
  abstract = {To further improve on the competitiveness of the boundary element method (BEM), a hybrid version of it is used for a numerical solution of two dimensional nonlinear coupled viscous Burger’s equation. Adopting this approach to a discretized 2D spatial domain, the resulting integral equations arising from the singular integral theory are applied locally to each of the elements. The resulting nonlinear discrete equations are finally solved by the Picard iteration algorithm. The simulation results obtained, not only concur with analytical solutions, but also display high accuracy and are in agreement with those available in literature.},
 year = {2017}
}

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TY  - JOUR
T1  - An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case
AU  - Okey Oseloka Onyejekwe
Y1  - 2017/01/24
PY  - 2017
N1  - https://doi.org/10.11648/j.ijfmts.20170301.11
DO  - 10.11648/j.ijfmts.20170301.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 1
EP  - 15
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20170301.11
AB  - To further improve on the competitiveness of the boundary element method (BEM), a hybrid version of it is used for a numerical solution of two dimensional nonlinear coupled viscous Burger’s equation. Adopting this approach to a discretized 2D spatial domain, the resulting integral equations arising from the singular integral theory are applied locally to each of the elements. The resulting nonlinear discrete equations are finally solved by the Picard iteration algorithm. The simulation results obtained, not only concur with analytical solutions, but also display high accuracy and are in agreement with those available in literature.
VL  - 3
IS  - 1
ER  -

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Author Information

Okey Oseloka Onyejekwe

Computational Science Program Addis Ababa University Arat Kilo Campus, Addis Ababa, Ethiopia

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Okey Oseloka Onyejekwe. (2017). An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case. International Journal of Fluid Mechanics & Thermal Sciences, 3(1), 1-15. https://doi.org/10.11648/j.ijfmts.20170301.11

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ACS Style

Okey Oseloka Onyejekwe. An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case. Int. J. Fluid Mech. Therm. Sci. 2017, 3(1), 1-15. doi: 10.11648/j.ijfmts.20170301.11

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AMA Style

Okey Oseloka Onyejekwe. An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case. Int J Fluid Mech Therm Sci. 2017;3(1):1-15. doi: 10.11648/j.ijfmts.20170301.11

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@article{10.11648/j.ijfmts.20170301.11,
  author = {Okey Oseloka Onyejekwe},
  title = {An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {3},
  number = {1},
  pages = {1-15},
  doi = {10.11648/j.ijfmts.20170301.11},
  url = {https://doi.org/10.11648/j.ijfmts.20170301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20170301.11},
  abstract = {To further improve on the competitiveness of the boundary element method (BEM), a hybrid version of it is used for a numerical solution of two dimensional nonlinear coupled viscous Burger’s equation. Adopting this approach to a discretized 2D spatial domain, the resulting integral equations arising from the singular integral theory are applied locally to each of the elements. The resulting nonlinear discrete equations are finally solved by the Picard iteration algorithm. The simulation results obtained, not only concur with analytical solutions, but also display high accuracy and are in agreement with those available in literature.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case
AU  - Okey Oseloka Onyejekwe
Y1  - 2017/01/24
PY  - 2017
N1  - https://doi.org/10.11648/j.ijfmts.20170301.11
DO  - 10.11648/j.ijfmts.20170301.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 1
EP  - 15
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20170301.11
AB  - To further improve on the competitiveness of the boundary element method (BEM), a hybrid version of it is used for a numerical solution of two dimensional nonlinear coupled viscous Burger’s equation. Adopting this approach to a discretized 2D spatial domain, the resulting integral equations arising from the singular integral theory are applied locally to each of the elements. The resulting nonlinear discrete equations are finally solved by the Picard iteration algorithm. The simulation results obtained, not only concur with analytical solutions, but also display high accuracy and are in agreement with those available in literature.
VL  - 3
IS  - 1
ER  -

Copy | Download