Dispersive Groundwater Flow and Pollution
In this chapter we apply the asymptotic approximation method of the previous chapter to the problem of arrival of contaminants in the groundwater at a pumping well. For the study of groundwater pollution it is not sufficient to model the transport of particles by advection only. In addition the mechanism of macroscopic dispersion has to be taken in consideration. It accounts for the random motion of individual particles in the flow. In this study we assume that the hydrodynamic dispersion is proportional to the velocity with coefficients a L in the longitudinal direction and a T in the transversal direction, see Bear and Verruijt (1987). We analyse the properties of the random walk model for particles from the Fokker—Planck equation. The concentration function for a pollutant is interpreted as the space-time probability density function for a contaminated water particle as it makes a random walk. We will take a L and a T constant. The method also applies to spatial heterogeneous dispersion constants, see Van Kooten (1996).
KeywordsBoundary Layer Stagnation Point Random Walk Model Outer Solution Boundary Layer Solution
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