ABSTRACT
Van Genuchten and Alves have provided a compendium of many analytical solutions to the advection-diffusion equation. This chapter summarizes several of these solutions and discusses the numerical evaluation of the solutions. It outlines the system equations were solved using a Laplace transform technique. In many environmental situations it is not possible to neglect advection, even for vertical transport through multilayered media. The contaminated mobile phase may be subject to advective forces in addition to basic diffusive/dispersive forces. The advection-diffusion equation may be used to model experiments which are used in determining important properties of the sediment being studied. The advection-diffusion equation is solved using a Laplace transform technique. The solution procedures follow the same pattern whereby the integrated form of the ordinary differential equation is required to be known beforehand due to the complexity of the boundary value problem.
