A numerical, grid-element model has been developed for the study of air pollution transport from urban area-type sources. This advection-diffusion model is especially useful for the estimation of air pollution concentrations under conditions of spatial and time varying emissions, velocities and diffusion rates. The “pseudo-diffusive” errors associated with conventional finite-difference approximations to advective transport are eliminated by a material-conserving computation procedure involving the zeroth, first and second moments of the concentration distribution within each grid element. Extensions of the procedure are suggested for retention of sub-grid-scale resolution of concentration values necessary in the study of transport of chemically reactive materials, or for the incorporation of emissions from point and line sources. A novel procedure is presented for the numerical simulation of horizontal diffusion from area sources which can be used to model empirically observed dispersive growth rates.