Numerical Solution of Fractional Advection-Dispersion Equation
Publication: Journal of Hydraulic Engineering
Volume 130, Issue 5
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 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 Central Scheme” possessing the F-th order accuracy—are presented for fractional order derivatives. The 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 scheme can accurately simulate the long-tailed dispersion processes in natural rivers.
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Published In
Journal of Hydraulic Engineering
Volume 130 • Issue 5 • May 2004
Pages: 422 - 431
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: May 23, 2002
Accepted: Oct 30, 2003
Published online: Apr 15, 2004
Published in print: May 2004
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