Transport by Advection and Dispersion

Abstract

In the previous chapter, numerical models for the main mechanism of transport in porous media — advection — were presented. In reality, the transport of particles of a component of a pollutant is also influenced by diffusion and dispersion, which cause a spreading of the pollutant over an ever-growing region. Thus, the groundwater may be polluted over a much larger region than in the case of pure advection, with a corresponding reduction in the maximum and average concentrations of the pollutant. The conceptual and mathematical modeling of these phenomena are discussed in Chapter 6. In this chapter, some numerical models for the quantitative analysis of transport by advection and dispersion are presented. These include a fully numerical two-dimensional method, and a semi-analytical method, using a random walk model. For didactic reasons, the simple one-dimensional case will be considered first. This case is discussed in order to show that the numerical analysis of dispersion may involve a rather disturbing influence of discretization, i.e., numerical dispersion which should be recognized and, if possible, reduced, or at least controlled.