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Numerical solution of fractional advection-dispersion equation

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Author

Summary, in English

Numerical schemes and stability criteria are developed for solution of the one-dimensional fractional advection-dispersion equation (FRADE) derived by revising Fick's first law. Employing 74 sets of dye test data measured on natural streams, it is found that the fractional order F of the partial differential operator acting on the dispersion term varies around the most frequently occurring value of F = 1.65 in the range of 1.4 to 2.0. Two series expansions are proposed for approximation of the limit definitions of fractional derivatives. On this ground, two three-term finite-difference schemes-"1.3 Backward Scheme" having the first-order accuracy and "F.3 Central Scheme" possessing the F-th order accuracy-are presented for fractional order derivatives. The F.3 scheme is found to perform better than does the 1.3 scheme in terms of error and stability analyses and is thus recommended for numerical solution of FRADE. The fractional dispersion model characterized by the FRADE and the F.3 scheme can accurately simulate the long-tailed dispersion processes in natural rivers.

Publishing year

2004

Language

English

Pages

422-431

Publication/Series

Journal of Hydraulic Engineering

Volume

130

Issue

5

Document type

Journal article

Publisher

American Society of Civil Engineers (ASCE)

Topic

  • Water Engineering

Keywords

  • numerical models
  • wave dispersion
  • rivers
  • advection
  • stability analysis

Status

Published

ISBN/ISSN/Other

  • ISSN: 1943-7900