Mathematical models for pollutant transport in semi-infinite aquifers are based on the advection-dispersion equation (ADE) and its variants. This study employs the ADE incorporating time-dependent dispersion and velocity and space-time dependent source and sink, expressed by one function. The dispersion theory allows mechanical dispersion to be directly proportional to seepage velocity. Initial...

Mathematical models for pollutant transport in semi-infinite aquifers are based on the advection-dispersion equation (ADE) and its variants. This study employs the ADE incorporating time-dependent dispersion and velocity and space-time dependent source and sink, expressed by one function. The dispersion theory allows mechanical dispersion to be directly proportional to seepage velocity. Initial...

This paper describes the development of the stream-tube based dispersion model for modeling contaminant transport in open channels. The operator-splitting technique is employed to separate the 2D contaminant transport equation into the pure advection and pure dispersion equations. Then the total variation diminishing (TVD) schemes are combined with the second-order Lax-Wendroff and third–order ...

the transport of dissolved contaminants in groundwater is usually described by the advectiondispersion equation with reaction. several numerical methods for solving the one-dimensional are availableincluding finite difference methods, finite volume methods, and finite element methods. stringent conditions,such as small peclet (pe) and courant (cr) numbers, must be satisfied to ensure the accura...

A mathematical model presented in this paper describes the dispersion and concentration ofcontaminants (fine and coarse) in porous medium with the effect of chemical reaction. Solutetransport in porous media is discussed by means of advection-dispersion equation. The effectof particle mass parameter and reaction rate parameter on the dispersion coefficient and meanconcentration of a chemical so...

[1] We thank Lim [2005] for providing this opportunity to clarify the restrictions and confirm the applicability of the results of LaBolle et al. [2000]. LaBolle et al. [2000] develop generalized stochastic differential equations (SDE) that converge to advection dispersion equations with discontinuous dispersion tensor D. The problem of interest here relates to equation (15a) of LaBolle et al. ...

In the last three decades, interest in fractional calculus has experienced rapid growth and at present we can find many papers devoted its theoretical and application aspects (see the work of Machado et al. (2011) and the references therein). Fractional order models of real systems are often more adequate than the usually used integer order models in electrochemistry (Ichise et al., 1971), adve...

A transport equation that uses fractional-order dispersion derivatives has fundamental solutions that are Lévy’s a-stable densities. These densities represent plumes that spread proportional to time, have heavy tails, and incorporate any degree of skewness. The equation is parsimonious since the dispersion parameter is not a function of time or distance. The scaling behavior of plumes that unde...