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Research Papers

Fractional Convection

[+] Author and Article Information
Changpin Li

Department of Mathematics,
Shanghai University,
Shanghai 200444, China
e-mail: lcp@shu.edu.cn

Qian Yi

Department of Mathematics,
Shanghai University,
Shanghai 200444, China
e-mail: yiqian@i.shu.edu.cn

Jürgen Kurths

Potsdam Institute for Climate Impact Research,
Potsdam 14473, Germany
e-mail: Juergen.kurths@pik-potsdam.de

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 21, 2016; final manuscript received July 18, 2017; published online October 9, 2017. Assoc. Editor: Gabor Stepan.

J. Comput. Nonlinear Dynam 13(1), 011004 (Oct 09, 2017) (6 pages) Paper No: CND-16-1572; doi: 10.1115/1.4037414 History: Received November 21, 2016; Revised July 18, 2017

In this study, we describe the fractional convection operator for the first time and present its discrete form with second-order convergence. A numerical scheme for the fractional-convection–diffusion equation is also constructed in order to get insight into the fractional convection behavior visually. Then, we study the fractional-convection-dominated diffusion equation which has never been considered, where the diffusion is normal and is characterized by the Laplacian. The interesting fractional convection phenomena are observed through numerical simulation. Moreover, we investigate the fractional-convection-dominated-diffusion equation which is studied for the first time either, where the convection and the diffusion are both in the fractional sense. The corresponding fractional convection phenomena are displayed via computer graphics as well.

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References

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Figures

Grahic Jump Location
Fig. 1

The numerical solution surfaces of Eq. (23) with α=0.3,τ=1/100, and h=π/1000

Grahic Jump Location
Fig. 2

The numerical solution surfaces of Eq. (23) with ε=0.21,τ=1/100, and h=π/1000

Grahic Jump Location
Fig. 3

The numerical solution surfaces of Eq. (23) with ε=0.30,α=0.5,τ=1/100, and h=π/1000

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