Open AccessNumerical approach to simulate diffusion model of a fluid-flow in a porous media
Author(s) -
Y. Esmaeelzade Aghdam,
B. Farnam,
Hossein Jafari
Publication year - 2021
Publication title -
thermal science/thermal science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 2334-7163
pISSN - 0354-9836
DOI - 10.2298/tsci21s2255e
Subject(s) - fractional calculus , diffusion , dispersion (optics) , anomalous diffusion , brownian motion , porous medium , derivative (finance) , fractional brownian motion , space (punctuation) , convergence (economics) , flow (mathematics) , statistical physics , mechanics , particle (ecology) , order (exchange) , mathematics , physics , computer science , porosity , materials science , thermodynamics , statistics , geology , innovation diffusion , optics , knowledge management , oceanography , financial economics , composite material , operating system , economics , economic growth , finance
When a particle distributes at a rate that deviates from the classical Brownian motion model, fractional space derivatives have been used to simulate anomalous diffusion or dispersion. When a fractional derivative substitutes the second-order derivative in a diffusion or dispersion model, amplified diffusion occurs (named super-diffusion). The proposed approach in this paper allows seeing the physical background of the newly defined Caputo space-time-fractional derivative and indicates that the order of convergence to approximate such equations has increased.