Finite difference solution of the one-dimensional advection–diffusion equation with variable coefficients in semi-infinite media

One-dimensional advection–diffusion equation with variable coefficients in semi-infinite media is solved using explicit finite difference method for three dispersion problems: (i) solute dispersion along steady flow through inhomogeneous medium, (ii) temporally dependent solute dispersion along uniform flow through homogeneous medium, and (iii) solute dispersion along temporally dependent unsteady flow through inhomogeneous medium. The continuous point source of uniform nature is considered at the origin of the medium. Results are compared to analytical solutions reported in the literature and good agreement was found. We have shown that explicit finite difference method is effective and accurate for solving advection–diffusion equation with variable coefficients in semi-infinite media, which is especially important when arbitrary initial and boundary conditions are required.