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A short review on the homotopy analysis method in fluid mechanics

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Abstract

We give a short review on the current development of homotopy analysis method (HAM), an analytic technique for strongly nonlinear problems, and its applications in fluid mechanics.

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References

  1. Liao S J. Proposed homotopy analysis techniques for the solution of nonlinear problems, Ph. D. Thesis, Shanghai, Shanghai Jiaotong Univ., 1992.

    Google Scholar 

  2. Liao S J. An approximate solution technique which does not depend upon small parameters (Part 2): an application in fluid mechanics, Int. J. Non-Linear Mech., 1997, 32(5): 815–822.

    Article  Google Scholar 

  3. Liao S J. Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC Press, 2003.

  4. Liao S J, Tan Y. A general approach to obtain series solutions of nonlinear differential equation. Studies in Applied Mathematics, 2007, 119: 297–354.

    Article  MathSciNet  Google Scholar 

  5. Liao S J. Notes on the homotopy analysis method: Some definitions and theorems. Commun. Nonlinear Sci. Numer. Simulat., 2009, 14: 983–997

    Article  MathSciNet  Google Scholar 

  6. Liao S J. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simulat., online.

  7. Prandtl L. Uueber Fluessigkeitsbewgungen bei sehr kleiner Reibung. Verhandlg. III. Int. Math. kongr. Heidelberg, 1904: 484–491

  8. Kousar N, Liao S J. Series solution of non-similarity boundary-layer flows over a porous wedge. Transp. Porous Med. (online)

  9. Hang X, Lin Z L, Liao S J, et al. Homotopy-based solutions of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Physics of Fluids (online)

  10. Cheng J, Cang J, Liao S J. On the interaction of deep water waves and exponential shear currents. Z. angew. Math. Phys., 2009, 60: 450–478.

    Article  MathSciNet  Google Scholar 

  11. Phillips OM. On the dynamics of unsteady gravity waves of finite amplitude. Part 1: The elementary interactions. J. Fluid Mech., 1960, 9: 193–217.

    Article  MathSciNet  Google Scholar 

  12. Liao SJ. On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves. arXiv:1005.5539.

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Authors and Affiliations

  1. State Key Lab of Ocean Engineering, Shanghai Jiaotong University, Shanghai, China

    Sh-ijun Liao

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  1. Sh-ijun Liao
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Correspondence to Sh-ijun Liao.

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Liao, Si. A short review on the homotopy analysis method in fluid mechanics. J Hydrodyn 22 (Suppl 1), 839–841 (2010). https://doi.org/10.1016/S1001-6058(10)60046-7

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  • DOI: https://doi.org/10.1016/S1001-6058(10)60046-7

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