Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finite-difference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity). Included are the first-order decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in finite media, which is especially important when arbitrary initial and boundary conditions are required.