Migration of pollutants in groundwater. II: Adsorbable pollutants and numerical dispersion reduction

We discuss here the partial differential equations governing the migration of a decomposing pollutant adsorbing according to a Langmuir isotherm and undergoing 2-dimensional flow in a saturated aquifer. The equation governing the mass transfer of the pollutant to the surfaces within the aquifer are solved in closed form, permitting the use of larger values of the time increment Δt in the numerical integration of the dispersion-advection equation governing the behavior of the dissolved pollutant. In this numerical integration transverse numerical dispersion is eliminated by using conformal coordinates (velocity potential and stream function), and longitudinal numerical dispersion is very substantially reduced by use of an asymmetrical 4-point formula to represent the advection term. Some representative results are given as contour maps. The mass transfer rate coefficient is estimated as the least positive eigenvalue of a diffusion problem.