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

[摘要] The transport of chemicals through soils to the groundwater or precipitationat 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 longrun. In this dissertation, we consider macroscopic deterministic models de-scribing contaminant transport in saturated soils under uniform radial waterow backgrounds. The arising convection-dispersion equation given in termsof the stream functions is analyzed using classical Lie point symmetries. Anumber of exotic Lie point symmetries are admitted. Group invariant solu-tions are classi ed according to the elements of the one-dimensional optimalsystems. We analyze the group invariant solutions which satisfy some physicalboundary conditions.The governing equation describing movements of contaminants under ra-dial water ow background may be given in conserved form. As such, theconserved form of the governing equation may be written as a system ofrstorder partial di erential equation referred to as an auxiliary system, by an in-troduction of the nonlocal variable. The resulting system of equations admitsa number of (local) point symmetries which induce the nonlocal symmetriesfor the original governing equation. We construct classes of solutions using theadmitted genuine nonlocal symmetries, which include the invariant solutionsobtained via corresponding point symmetries of the governing equation.

[发布机构] University of the Witwatersrand