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research-article

Fractional convection

[+] Author and Article Information
Changpin Li

Department of Mathematics, Shanghai University, Shanghai 200444, China
lcp@shu.edu.cn

Qian Yi

Department of Mathematics, Shanghai University, Shanghai 200444, China
yiqian@i.shu.edu.cn

J̈urgen Kurths

Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
juergen.kurths@pik-potsdam.de

1Corresponding author.

ASME doi:10.1115/1.4037414 History: Received November 21, 2016; Revised July 18, 2017

Abstract

We clearly describe the fractional convection operator for the first time and present its discrete form with 2nd-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 is observed through numerical simulation. Moreover, we continue to 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 according fractional convection phenomena is displayed via computer graphics as well.

Copyright (c) 2017 by ASME
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