Numerical Analysis Seminars: Numerical solution for transport equations with anomalous diffusion
3 February 2012 14:00 in CG83Analysis of diffusion in a complex environment shows that the conventional diffusion, characterized by the Brownian motion, fails to model the anomalous character of the diffusive mass transport observed in many experiments. Therefore new mathematical models were proposed and validated. In this work, we consider a fractional advection diffusion model where the usual second-order derivative gives place to a fractional derivative of order $\alpha$, with $ 1<\alpha \leq 2$. When a fractional derivative replaces the second order derivative in a diffusion or dispersion model, it leads to enhanced diffusion, also called superdiffusion. We present a numerical method to solve this model and additionally some physical properties are simulated.
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