Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/44968
Title: | Super-diffusive Transport Processes in Porous Media | Authors: | Sousa, Ercília | Issue Date: | 2013 | Publisher: | Springer | Project: | PEst-C/MAT/UI0324/2011 | Serial title, monograph or event: | Modelling and Simulation in Fluid Dynamics in Porous Media. Springer Proceedings in Mathematics & Statistics. | Volume: | 28 | Abstract: | The basic assumption of models for the transport of contaminants through soil is that the movements of solute particles are characterized by the Brownian motion. However, the complexity of pore space in natural porous media makes the hypothesis of Brownian motion far too restrictive in some situations. Therefore, alternative models have been proposed. One of the models, many times encountered in hydrology, is based in fractional differential equations, which is a one-dimensional fractional advection diffusion equation where the usual second-order derivative gives place to a fractional derivative of order α, with 1 < α ≤ 2. When a fractional derivative replaces the second-order derivative in a diffusion or dispersion model, it leads to anomalous diffusion, also called super-diffusion. We derive analytical solutions for the fractional advection diffusion equation with different initial and boundary conditions. Additionally, we analyze how the fractional parameter α affects the behavior of the solutions. | URI: | https://hdl.handle.net/10316/44968 | DOI: | 10.1007/978-1-4614-5055-9_5 10.1007/978-1-4614-5055-9_5 |
Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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