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 - <p style="text-align: justify;">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&#39; 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.</p>