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Volume 36, Issue 4
Anomalous Diffusion in Finite Length Fingers Comb Frame with the Effects of Time and Space Riesz Fractional Cattaneo-Christov Flux and Poiseuille Flow

Lin Liu, Liancun Zheng, Fawang Liu & Xinxin Zhang

DOI: 10.4208/jcm.1702-m2016-0627

J. Comp. Math., 36 (2018), pp. 563-578.

Published online: 2018-06

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  • Abstract

This paper presents an investigation on the anomalous diffusion in finite length fingers comb frame, the time and space Riesz fractional Cattaneo-Christov flux is introduced with the Oldroyds' upper convective derivative and the effect of Poiseuille flow is also taken into account. Formulated governing equation possesses the coexisting characteristics of parabolicity and hyperbolicity. Numerical solution is obtained by the L1-scheme and shifted Grünwald formulae, which is verified by introducing a source item to construct an exact solution. The effects, such as time and space fractional parameters, relaxation parameter and the ratio of the pressure gradient and viscosity coefficient, on the spatial and temporal evolution of particles distribution and dynamic characteristics are shown graphically and analyzed in detail.

  • Keywords

Anomalous diffusion, Cattaneo-Christov flux, Fractional derivative, Poiseuille flow, Distribution.

  • AMS Subject Headings

60J60, 97M10, 35R11, 92E20, 97K60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

liulin1020@126.com (Lin Liu)

liancunzheng@ustb.edu.cn (Liancun Zheng)

F.liu@qut.edu.au (Fawang Liu)

xxzhang@ustb.edu.cn (Xinxin Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-563, author = {Liu , LinZheng , LiancunLiu , Fawang and Zhang , Xinxin}, title = {Anomalous Diffusion in Finite Length Fingers Comb Frame with the Effects of Time and Space Riesz Fractional Cattaneo-Christov Flux and Poiseuille Flow}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {4}, pages = {563--578}, abstract = {

This paper presents an investigation on the anomalous diffusion in finite length fingers comb frame, the time and space Riesz fractional Cattaneo-Christov flux is introduced with the Oldroyds' upper convective derivative and the effect of Poiseuille flow is also taken into account. Formulated governing equation possesses the coexisting characteristics of parabolicity and hyperbolicity. Numerical solution is obtained by the L1-scheme and shifted Grünwald formulae, which is verified by introducing a source item to construct an exact solution. The effects, such as time and space fractional parameters, relaxation parameter and the ratio of the pressure gradient and viscosity coefficient, on the spatial and temporal evolution of particles distribution and dynamic characteristics are shown graphically and analyzed in detail.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1702-m2016-0627}, url = {http://global-sci.org/intro/article_detail/jcm/12305.html} }
TY - JOUR T1 - Anomalous Diffusion in Finite Length Fingers Comb Frame with the Effects of Time and Space Riesz Fractional Cattaneo-Christov Flux and Poiseuille Flow AU - Liu , Lin AU - Zheng , Liancun AU - Liu , Fawang AU - Zhang , Xinxin JO - Journal of Computational Mathematics VL - 4 SP - 563 EP - 578 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1702-m2016-0627 UR - https://global-sci.org/intro/article_detail/jcm/12305.html KW - Anomalous diffusion, Cattaneo-Christov flux, Fractional derivative, Poiseuille flow, Distribution. AB -

This paper presents an investigation on the anomalous diffusion in finite length fingers comb frame, the time and space Riesz fractional Cattaneo-Christov flux is introduced with the Oldroyds' upper convective derivative and the effect of Poiseuille flow is also taken into account. Formulated governing equation possesses the coexisting characteristics of parabolicity and hyperbolicity. Numerical solution is obtained by the L1-scheme and shifted Grünwald formulae, which is verified by introducing a source item to construct an exact solution. The effects, such as time and space fractional parameters, relaxation parameter and the ratio of the pressure gradient and viscosity coefficient, on the spatial and temporal evolution of particles distribution and dynamic characteristics are shown graphically and analyzed in detail.

Liu , LinZheng , LiancunLiu , Fawang and Zhang , Xinxin. (2018). Anomalous Diffusion in Finite Length Fingers Comb Frame with the Effects of Time and Space Riesz Fractional Cattaneo-Christov Flux and Poiseuille Flow. Journal of Computational Mathematics. 36 (4). 563-578. doi:10.4208/jcm.1702-m2016-0627
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