Group invariant solutions for contaminant transport in saturated soils under radial uniform water flow background

Abstract

The transport of chemicals through soils to the groundwater or precipitation at the soils surfaces leads to degradation of the resources such as soil fertility, drinking water and so on. Serious consequences may be su ered in the long run. In this dissertation, we consider macroscopic deterministic models de- scribing contaminant transport in saturated soils under uniform radial water

ow backgrounds. The arising convection-dispersion equation given in terms of the stream functions is analyzed using classical Lie point symmetries. A number of exotic Lie point symmetries are admitted. Group invariant solu- tions are classi ed according to the elements of the one-dimensional optimal systems. We analyze the group invariant solutions which satisfy some physical boundary conditions. The governing equation describing movements of contaminants under ra- dial water ow background may be given in conserved form. As such, the conserved form of the governing equation may be written as a system of rst order partial di erential equation referred to as an auxiliary system, by an in- troduction of the nonlocal variable. The resulting system of equations admits a number of (local) point symmetries which induce the nonlocal symmetries for the original governing equation. We construct classes of solutions using the admitted genuine nonlocal symmetries, which include the invariant solutions obtained via corresponding point symmetries of the governing equation.