Application of the Adomian Decomposition Method to Oscillating Viscous Flows

Chi-Min Liu

doi:doi:10.11648/j.acm.20160503.15

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Application of the Adomian Decomposition Method to Oscillating Viscous Flows

Chi-Min Liu

Published in Applied and Computational Mathematics (Volume 5, Issue 3)

Received: 3 June 2016 Accepted: 13 June 2016 Published: 29 June 2016

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Abstract

In this paper three oscillating viscous flows are studied by applying the Adomian decomposition method (ADM). Major improvement is on the choice of the assignment of the first term of the decomposition series. Different from past studies in which the initial velocity profile of the whole domain is assigned as the first term of the decomposition series, the assignment in present study is simply the boundary velocity for Stokes’ second problem and the pressure gradient for pulsatile flows. This improvement demonstrates and implies that ADM is not only good in approaching the known exact solution, but also possesses the practicability in treating realistic problems. The derived approximate solutions accurate up to any order can be obtained after two key parameters are determined. Present results show an excellent agreement with those calculated by the exact solutions. Based on the present results, more periodic problems can be analyzed by ADM with the help of Fourier analysis.

Published in	Applied and Computational Mathematics (Volume 5, Issue 3)
DOI	10.11648/j.acm.20160503.15
Page(s)	121-132
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), 2016. Published by Science Publishing Group

Keywords

Adomian Decomposition Method, Stokes’ Second Problem, Pulsatile Flow, Starting Assignment

References

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APA Style

Chi-Min Liu. (2016). Application of the Adomian Decomposition Method to Oscillating Viscous Flows. Applied and Computational Mathematics, 5(3), 121-132. https://doi.org/10.11648/j.acm.20160503.15

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ACS Style

Chi-Min Liu. Application of the Adomian Decomposition Method to Oscillating Viscous Flows. Appl. Comput. Math. 2016, 5(3), 121-132. doi: 10.11648/j.acm.20160503.15

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AMA Style

Chi-Min Liu. Application of the Adomian Decomposition Method to Oscillating Viscous Flows. Appl Comput Math. 2016;5(3):121-132. doi: 10.11648/j.acm.20160503.15

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@article{10.11648/j.acm.20160503.15,
  author = {Chi-Min Liu},
  title = {Application of the Adomian Decomposition Method to Oscillating Viscous Flows},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {3},
  pages = {121-132},
  doi = {10.11648/j.acm.20160503.15},
  url = {https://doi.org/10.11648/j.acm.20160503.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160503.15},
  abstract = {In this paper three oscillating viscous flows are studied by applying the Adomian decomposition method (ADM). Major improvement is on the choice of the assignment of the first term of the decomposition series. Different from past studies in which the initial velocity profile of the whole domain is assigned as the first term of the decomposition series, the assignment in present study is simply the boundary velocity for Stokes’ second problem and the pressure gradient for pulsatile flows. This improvement demonstrates and implies that ADM is not only good in approaching the known exact solution, but also possesses the practicability in treating realistic problems. The derived approximate solutions accurate up to any order can be obtained after two key parameters are determined. Present results show an excellent agreement with those calculated by the exact solutions. Based on the present results, more periodic problems can be analyzed by ADM with the help of Fourier analysis.},
 year = {2016}
}

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TY  - JOUR
T1  - Application of the Adomian Decomposition Method to Oscillating Viscous Flows
AU  - Chi-Min Liu
Y1  - 2016/06/29
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160503.15
DO  - 10.11648/j.acm.20160503.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 121
EP  - 132
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160503.15
AB  - In this paper three oscillating viscous flows are studied by applying the Adomian decomposition method (ADM). Major improvement is on the choice of the assignment of the first term of the decomposition series. Different from past studies in which the initial velocity profile of the whole domain is assigned as the first term of the decomposition series, the assignment in present study is simply the boundary velocity for Stokes’ second problem and the pressure gradient for pulsatile flows. This improvement demonstrates and implies that ADM is not only good in approaching the known exact solution, but also possesses the practicability in treating realistic problems. The derived approximate solutions accurate up to any order can be obtained after two key parameters are determined. Present results show an excellent agreement with those calculated by the exact solutions. Based on the present results, more periodic problems can be analyzed by ADM with the help of Fourier analysis.
VL  - 5
IS  - 3
ER  -

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Author Information

Chi-Min Liu

Division of Mathematics, General Education Center, Chienkuo Technology University, Changhua City, Taiwan

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APA Style

Chi-Min Liu. (2016). Application of the Adomian Decomposition Method to Oscillating Viscous Flows. Applied and Computational Mathematics, 5(3), 121-132. https://doi.org/10.11648/j.acm.20160503.15

Copy | Download

ACS Style

Chi-Min Liu. Application of the Adomian Decomposition Method to Oscillating Viscous Flows. Appl. Comput. Math. 2016, 5(3), 121-132. doi: 10.11648/j.acm.20160503.15

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AMA Style

Chi-Min Liu. Application of the Adomian Decomposition Method to Oscillating Viscous Flows. Appl Comput Math. 2016;5(3):121-132. doi: 10.11648/j.acm.20160503.15

Copy | Download

@article{10.11648/j.acm.20160503.15,
  author = {Chi-Min Liu},
  title = {Application of the Adomian Decomposition Method to Oscillating Viscous Flows},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {3},
  pages = {121-132},
  doi = {10.11648/j.acm.20160503.15},
  url = {https://doi.org/10.11648/j.acm.20160503.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160503.15},
  abstract = {In this paper three oscillating viscous flows are studied by applying the Adomian decomposition method (ADM). Major improvement is on the choice of the assignment of the first term of the decomposition series. Different from past studies in which the initial velocity profile of the whole domain is assigned as the first term of the decomposition series, the assignment in present study is simply the boundary velocity for Stokes’ second problem and the pressure gradient for pulsatile flows. This improvement demonstrates and implies that ADM is not only good in approaching the known exact solution, but also possesses the practicability in treating realistic problems. The derived approximate solutions accurate up to any order can be obtained after two key parameters are determined. Present results show an excellent agreement with those calculated by the exact solutions. Based on the present results, more periodic problems can be analyzed by ADM with the help of Fourier analysis.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Application of the Adomian Decomposition Method to Oscillating Viscous Flows
AU  - Chi-Min Liu
Y1  - 2016/06/29
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160503.15
DO  - 10.11648/j.acm.20160503.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 121
EP  - 132
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160503.15
AB  - In this paper three oscillating viscous flows are studied by applying the Adomian decomposition method (ADM). Major improvement is on the choice of the assignment of the first term of the decomposition series. Different from past studies in which the initial velocity profile of the whole domain is assigned as the first term of the decomposition series, the assignment in present study is simply the boundary velocity for Stokes’ second problem and the pressure gradient for pulsatile flows. This improvement demonstrates and implies that ADM is not only good in approaching the known exact solution, but also possesses the practicability in treating realistic problems. The derived approximate solutions accurate up to any order can be obtained after two key parameters are determined. Present results show an excellent agreement with those calculated by the exact solutions. Based on the present results, more periodic problems can be analyzed by ADM with the help of Fourier analysis.
VL  - 5
IS  - 3
ER  -

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