Document Type
Article
Publication Date
1-1-2004
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.
Publication Source (Journal or Book title)
Journal of Hydraulic Engineering
First Page
422
Last Page
431
Recommended Citation
Deng, Z., Singh, V., & Bengtsson, L. (2004). Numerical Solution of Fractional Advection-Dispersion Equation. Journal of Hydraulic Engineering, 130 (5), 422-431. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:5(422)