Mass spreading of non-reactive tracers in fractured bedrock can be described by a combination of molecular diffusion, hydrodynamic dispersion, and heterogeneous advection. These spreading mechanisms are fundamentally different in their behavior and, therefore, must be measured separately for reliable predictions of transport to be made. To separate the influence of these mechanisms, to the exte...

This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie's modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, m...

The stationary fractional advection dispersion equation is discretized by linear finite element scheme, and a full V-cycle multigrid method (FV-MGM) is proposed to solve the resulting system. Some useful properties of the approximation and smoothing operators are proved. Using these properties we derive the convergence results in both L2 norm and energy norm for FV-MGM. Numerical examples are g...

In this paper, by combining of fractional centered difference approach with alternating direction implicit method, we introduce a mixed method for solving two-dimensional Riesz space advection-dispersion equation. The proposed is fourth order operator in spatial directions and second Crank-Nicolson temporal direction. By reviewing the consistency stability convergen...