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Note on Barenblatt power series solution to Boussinesq equation

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Abstract

To the self-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Ocean College, Hohai University, Nanjing, 210098, P. R. China

    Song Zhi-yao  (宋志尧) (Professor, Doctor)

  2. Center for Eco-environmental Modelling, Hohai University, Nanjing, 210098, P. R. China

    Song Zhi-yao  (宋志尧) (Professor, Doctor) & Li Ling  (李凌)

  3. School of Engineering, The University of Queensland, Qld, 4072, Australia

    Li Ling  (李凌) & David Lockington

  4. Key Laboratory of Virtual Geographic Environment (Ministry of Education), Nanjing Normal University, Nanjing, 210097, P. R. China

    Song Zhi-yao  (宋志尧) (Professor, Doctor)

Authors
  1. Song Zhi-yao  (宋志尧)
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  2. Li Ling  (李凌)
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  3. David Lockington
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Corresponding author

Correspondence to Song Zhi-yao  (宋志尧).

Additional information

Communicated by HE You-sheng

Project supported by the National Natural Science Foundation of China (No.50425926)

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Song, Zy., Li, L. & David, L. Note on Barenblatt power series solution to Boussinesq equation. Appl Math Mech 28, 823–828 (2007). https://doi.org/10.1007/s10483-007-0612-x

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  • DOI: https://doi.org/10.1007/s10483-007-0612-x

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