Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows

Abstract

The transport of chemicals through soils to the groundwater or precipitation at the soils surfaces leads to degradation of these resources. Serious consequences may be suffered in the long run. In this paper, we consider macroscopic deterministic models describing contaminant transport in saturated soils under uniform radial water flow 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 solutions are classified according to the elements of the one-dimensional optimal systems. We analyzed the group invariant solutions which satisfy the physical boundary conditions.

Analytical Solutions of the Balance Equation for the Scalar Variance in One-Dimensional Turbulent Flows under Stationary Conditions

“…Several authors (e.g., [40,41]) presented analytical solutions on the scalar transport in fluid flows. Here, some of them are reported to compute the mean scalar gradient, which is a key input parameter for the analytical solutions of the concentration variance.…”

Evaluation of groundwater pollution in a mining area using analytical solution: a case study of the Yimin open-pit mine in China

“…A mathematical model about contaminant transport due to well injection was developed by Hsieh and Yeh ( 2014 ) in a confined aquifer. Potsane et al ( 2014 ) considered macroscopic deterministic models that describe contaminant transport in saturated soils, under uniform radial water flow conditions, through comparisons with numerical solutions.…”