Numerical solution of non-linear advection-dispersion equation in a finite porous domain

This study presents a numerical simulation of the one-dimensional concentration-dependent convection-dispersion equation in a finite heterogeneous porous formation. The solution of the convection-diffusion equation with variable coefficients is obtained with the help of MATLAB pdepe solver. The groundwater flow velocity depends on the pollutant concentration, and the dispersion coefficient is proportional to the groundwater flow velocity. The effects of the zero-order production term and the first-order decay are also considered. The aquifer is assumed to be heterogeneous and finite, with sources concentrated in the flow direction. It is assumed that the porous media and the pollutant are chemically non-reactive. Initially porous domain is considered not solute free. The model assumes a uniform continuous input point source and a variable input point source released from the left end of the aquifer domain. The obtained results graphically describe the importance of the dispersion coefficient and other relevant parameters for solute transport in porous media. The developed numerical solution is verified with an analytical solution, and it is found that they are in good agreement.