Analytical and three level implicit difference schemes for dispersion problem through porous media flow

Abstract

A mathematical model for the dispersion process in unsteady seepage flow through a porous domain is formulated. An analytical solution is obtained by using direct relationship between the dispersion coefficient and seepage velocity, and introducing a new time variable. Three, three-level implicit finite-difference schemes are also derived for the same model. The numerical results are compared with the analytical results and with a three-level explicit scheme. The comparison shows the implicit schemes to be more accurate compared to the analytical results.