Analytical solutions to two-dimensional advection-dispersion equation in cylindrical coordinates in finite domain subject to first- and third-type inlet boundary conditions

Jui Sheng Chen, Juan Tse Chen, Chen Wuing Liu, Ching Ping Liang, Chien Wen Lin

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41 Scopus citations

Abstract

This study presents exact analytical solutions to the two-dimensional advection-dispersion equation in cylindrical coordinates in finite domain subject to the first- and third-type inlet boundary conditions. The second kind finite Hankel transform and the generalized integral transform technique are adopted to solve the two-dimensional advection-dispersion equation in cylindrical coordinates and its associated initial and boundary conditions. The developed analytical solutions are compared with the solutions for semi-infinite domain subject to the first- and third-type inlet boundary conditions available in literature to illustrate the impacts of the exit boundary conditions. Results show that significant discrepancies between the breakthrough curves obtained from analytical solutions for the finite domain and infinite domain for small Peclet number. Numerical evaluations of the developed analytical solutions for finite domain are computationally intensive because that the convergences of the series progress slowly for medium Peclet number. The developed solutions should be especially useful for testing numerical model simulated solutions for the finite domain subject to first- and third-type inlet boundary conditions.

Original languageEnglish
Pages (from-to)522-531
Number of pages10
JournalJournal of Hydrology
Volume405
Issue number3-4
DOIs
StatePublished - 5 Aug 2011

Keywords

  • Advection-dispersion equation
  • Analytical solution
  • Cylindrical coordinates
  • Finite domain
  • Finite Hankel transform technique
  • Generalized integral transform technique (GITT)

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