Applied and Computational Mathematics

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Application of the Adomian Decomposition Method to Oscillating Viscous Flows

Received: 03 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.

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

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

References
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Author Information
  • Division of Mathematics, General Education Center, Chienkuo Technology University, Changhua City, Taiwan

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    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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    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://download.sciencepg.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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    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.
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