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Numerical solution of fractional advection-dispersion equation

Deng, ZQ; Singh, VP and Bengtsson, Lars LU (2004) In Journal of Hydraulic Engineering 130(5). p.422-431
Abstract
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
numerical models, wave dispersion, rivers, advection, stability analysis
in
Journal of Hydraulic Engineering
volume
130
issue
5
pages
422 - 431
publisher
American Society of Civil Engineers (ASCE)
external identifiers
  • wos:000220980100005
  • scopus:2142755490
ISSN
1943-7900
DOI
10.1061/(ASCE)0733-9429(2004)130:5(422)
language
English
LU publication?
yes
id
06031709-0cb7-4473-b31b-08a084a2343f (old id 280951)
date added to LUP
2007-10-23 11:03:28
date last changed
2017-09-03 04:31:20
@article{06031709-0cb7-4473-b31b-08a084a2343f,
  abstract     = {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.},
  author       = {Deng, ZQ and Singh, VP and Bengtsson, Lars},
  issn         = {1943-7900},
  keyword      = {numerical models,wave dispersion,rivers,advection,stability analysis},
  language     = {eng},
  number       = {5},
  pages        = {422--431},
  publisher    = {American Society of Civil Engineers (ASCE)},
  series       = {Journal of Hydraulic Engineering},
  title        = {Numerical solution of fractional advection-dispersion equation},
  url          = {http://dx.doi.org/10.1061/(ASCE)0733-9429(2004)130:5(422)},
  volume       = {130},
  year         = {2004},
}