A novel high-order ADI method for 3D fractionalconvection–diffusion equations. (August 2015)

• Record Type: Journal Article
• Authors: Zhai, Shuying; Gui, Dongwei; Huang, Pengzhan; Feng, Xinlong
• Is Part Of: International communications in heat and mass transfer. Volume 66(2015:Aug.)
• Page Start: 212
• Page End: 217
• Publication Date: 2015-08
• Subjects: 3D fractional convection–diffusion equation -- Caputo fractional derivative -- Riemann–Liouville fractional integral -- High-order compact scheme -- ADI method; MSC -- 65M06 -- 65F10 -- 76M20 -- 76Rxx; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Heat -- Transmission; Mass transfer; Periodicals; 621.4022
• DOI: 10.1016/j.icheatmasstransfer.2015.05.028
• Languages: English
• ISSNs: 0735-1933

Abstract

Abstract: In this paper, a novel high-order alternating direction implicit (ADI) method is proposed for the three-dimensional (3D) fractional convection–diffusion equation with a temporal fractional-derivative α ∈ (0, 1). In order to keep the fourth order accuracy to approximate the second order derivatives and the desirable tridiagonal nature of the finite difference equations, we first propose a transformation to eliminate the convection terms. Then the Riemann–Liouville fractional integral operator is used to eliminate the temporal fractional-derivative. Finally, two ADI schemes with convergence order O τ min 1 + 2 α, 2 + h 4 and O τ 2 + h 4 are established respectively, where τ and h are the temporal and spatial step sizes. Numerical experiments are presented to show the high accuracy of the new method in comparison with the related works.