We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion equation with a memory term. We have shown the exponential decay of the passive tracer concentration, under suitable conditions for the velocity field and the pro...

Previous work showed how moving particles that rest along their trajectory lead to timenonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new advection–dispersion equation with an additional fractional time derivative of order between 1 and 2. Solutions...

We consider the space fractional advection-dispersion equation, which is obtained from the classical advection-diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulas for the discretisation of the fractional derivative, to numerically solve the equation on a f...

Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-water hydrology, are scattered across the literature, and not always well known. In this two-part s...

In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion process, governed by the Lévy-Feller advection-dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting...

[1] Space-fractional advection-dispersion models provide attractive alternatives to the classical advection-dispersion equation for model applications that exhibit early arrivals and plume skewness. This paper develops a flexible method for estimating the parameters of the fractional transport model on the basis of spatial plume snapshots or temporal breakthrough curve data. A particle-tracking...

The dispersion relation of the semi-discrete continuous and discontin-uous Galerkin formulations are analysed for the linear advection equation. In the context of an spectral/hp element discretisation on an equispaced mesh the problem can be reduced to a P P eigenvalue problem where P is the polynomial order. The analytical dispersion relationships for polynomial order up to P = 3 and the numer...

0022-1694/$ see front matter 2009 Elsevier B.V. A doi:10.1016/j.jhydrol.2009.11.008 * Corresponding author. Address: P-12, New Med 221005, India. Tel.: +91 9450541328. E-mail addresses: [email protected], naveen@ In the present study one-dimensional advection–diffusion equation with variable coefficients is solved for three dispersion problems: (i) solute dispersion along steady flow through...