Analysis of a solute transport model with non-constant dispersion

Abstract

A non-linear two dimensional convection-dispersion equation (CDE) plays a vital role in most mathematical model. Our study is based on the model arising from water contamination through oil spillage. The model contains the non-constant dispersion. We employ Lie symmetry method to reduce the CDE into a simpler ordinary differential equations (ODEs) and introduce the G/G1 and w = (z′)−1 techniques to determine the exact solutions. Furthermore if the ODE turns to be difficult to solve, we resort to transformation methods which reduce the ODEs to a more simpler first ODEs. Exact solutions are constructed.A non-linear two dimensional convection-dispersion equation (CDE) plays a vital role in most mathematical model. Our study is based on the model arising from water contamination through oil spillage. The model contains the non-constant dispersion. We employ Lie symmetry method to reduce the CDE into a simpler ordinary differential equations (ODEs) and introduce the G/G1 and w = (z′)−1 techniques to determine the exact solutions. Furthermore if the ODE turns to be difficult to solve, we resort to transformation methods which reduce the ODEs to a more simpler first ODEs. Exact solutions are constructed.