In this paper, an anomalous advection-dispersion model involving a new general Liouville–Caputo fractional-order derivative is addressed for the first time. The series solutions of the general fractional advection-dispersion equations are obtained with the aid of the Laplace transform. The results are given to demonstrate the efficiency of the proposed formulations to describe the anomalous adv...

The governing equation of longitudinal dispersion phenomenon of one-dimensional concentration distribution in fluid flow through porous media has been obtained in term of one-dimensional non-linear advection-diffusion equation. This equation has been converted in term of dimensionless non-linear Burger's equation with its derivative, and it is multiplied by small parameter   0,1   . This eq...

prediction of spatial and temporal variation of water quality is vital for managing pollutantsdisposal into the rivers. depletion of dissolved oxygen (do) takes place due to the consumption of oxygen bymicrobes to digest bio-degradable pollutants which enter a water course. reaeration takes place in a specificrate depending on do deficit. many investigators have formulated models as an alternat...

In this paper, a numerical solution of time fractional advection-dispersion equations are presented.The new implicit nite dierence methods for solving these equations are studied. We examinepractical numerical methods to solve a class of initial-boundary value fractional partial dierentialequations with variable coecients on a nite domain. Stability, consistency, and (therefore) convergenceof t...

The problem of dispersion, advection and adsorption of a tracer in a double-porosity reservoir due to tracer injection in a well with a steady, radially divergent flow field was solved for the case of constant tracer concentration in the injection well. Longitudinal dispersion and advection was assumed to dominate transport in the fracture system and tracer diffusion and adsorption klas assumed...

In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by . 0 = ∂ ∂ + ∂ ∂ x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised s...