Semi-analytical study of a one-dimensional contaminant flow in a finite medium

O.R Jimoh,Y.M Aiyesimi,M Jiya,G.A Bolarin

doi:10.4314/jasem.v21i3.9

Abstract

The Bubnov-Galerkin weighted residual method was used to solve a one-dimensional contaminant flow problem in this paper. The governing equation of the contaminant flow, which is characterized by advection, dispersion and adsorption was discretized and solved to obtain the semi-analytical solution. The adsorption isotherm was assumed to be of Freudlich type. The results obtained were expressed in graphical form to show the effect of change in the parameters on the concentration of the contaminants. From the analysis of the results, it was discovered that the contaminant concentration decreases with increase in the distance from the origin as the dispersion and velocity coefficient decrease.Keywords: Adsorption, advection, Bubnov-Galerkin weighted residuals, contaminant, dispersion

Highlights

We choose the following boundary and initial conditionsMethod of Solution: Bubnov-Galerkin Method: Galerkin method is one of the weighted residual methods which is used in solving differential equations
Contaminant transport in soil, groundwater and surface water has been in hydro-geological research history for many years
We provide a semi-analytical solution of the one-dimensional nonlinear contaminant flow

Summary

We choose the following boundary and initial conditions

Method of Solution: Bubnov-Galerkin Method: Galerkin method is one of the weighted residual methods which is used in solving differential equations. When the problem at hand is an ordinary differential equation, we call the method, Galerkin weighted residual method and it requires only one equation residual. The method of weighted residual requires two types of functions namely, the basic functions and weight functions The former is used to construct the trial solution while the latter is used as criterion to minimize the residual. In applying Bubnov-Galerkin method, the trial solution is chosen to satisfy the boundary conditions while the basic functions must satisfy the homogeneous boundary conditions. In solving the above problem (3), we apply the Galerkin weighted residual method precisely the Bubnov-Galerkin method.

The equation residual is RE

RESULTS AND DISCUSSION

Conclusion