We analyse dispersion of contaminants in turbulent boundary layer using centre manifold technique. The method describes long-term asymptotics of the contaminant concentration as it becomes spread across the entire layer and is weakly distorted by the velocity shear. The dispersion is investigated in two cases: (a) logarithmic and (b) power velocity profile across the layer according to a tradit...

Abstract: In this paper, a two-dimensional variable-order fractional advection-dispersion equation with variable coefficient is considered. The numerical method with first order temporal accuracy and first order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by using energy method. Finally, the results of a numerical example supports the theoret...

In this paper a theoretical framework for the Galerkin finite element approximation to the steady state fractional advection dispersion equation is presented. Appropriate fractional derivative spaces are defined and shown to be equivalent to the usual fractional dimension Sobolev spaces H. Existence and uniqueness results are proven, and error estimates for the Galerkin approximation derived. N...

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. After time discretization, we utilize collocation technique and implement a product integration method in order to simplify the evaluation of the terms involving spatial fractional order derivatives. Then utilizing Bernstein polynomials as basis, the problem is transformed into a linear ...

The transport mechanism of contaminated groundwater has been a problematic issue for many decades, mainly due to the bad impact of the contaminants on the quality of the groundwater system. In this paper, the exact solution of two-dimensional advection-dispersion equation (ADE) is derived for a semi-infinite porous media with spatially dependent initial and uniform/flux boundary conditions. The...

The transport mechanism of contaminated groundwater has been a problematic issue for many decades, mainly due to the bad impact of the contaminants on the quality of the groundwater system. In this paper, the exact solution of two-dimensional advection-dispersion equation (ADE) is derived for a semi-infinite porous media with spatially dependent initial and uniform/flux boundary conditions. The...