This study deals with a two-dimensional (2D) contaminant transport problem subject to depth varying input source in a finite homogeneous groundwater reservoir. A depth varying input source at the upstream boundary is assumed as the location of disposal site of the pollutant from where contaminant enters into the soil medium and ultimately to the groundwater reservoir. At the extreme boundary of the flow site, the concentration gradient of the contaminant is assumed to be zero. Contaminant dispersion is considered along the horizontal and vertical directions of the groundwater flow. The governing transport equation is the advection-dispersion equation (ADE) associated with linear sorption and first-order biological degradation. The ADE is solved analytically by adopting Laplace transform method. Crank-Nicolson scheme is also adopted for the numerical simulation of the modelled problem. In the graphical comparison of the analytical and numerical solutions, the numerical solution follows very closely with the analytical solution. Also, Root Mean Square (RMS) error and CPU run time are obtained to account for the performance of the numerical solution.


  • Two-dimensional contaminant transport is discussed in a finite homogeneous porous medium.

  • Exponentially decaying depth dependent source is assumed at the upstream of the domain.

  • The governing equation is solved analytically and numerically.

  • The RMS error is observed very less.

  • Verified the input data used in the present study from the existing literature.

Graphical Abstract

Graphical Abstract
Graphical Abstract
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