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.
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.
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Li, C., Yi, Q., and Kurths, J. (October 9, 2017). "Fractional Convection." ASME. J. Comput. Nonlinear Dynam. January 2018; 13(1): 011004. https://doi.org/10.1115/1.4037414
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