Abstract:
A mathematical backward problem which involves solving a mathematical model based on a one
dimensional advection - diffusion process of solute transport in a homogeneous soil structure is
considered. The diffusion coefficient and advection velocity in the governing unsteady non-linear
partial differential equation (PDE) are varied from constant to linearly dependent on time. This is
done to develop a mathematical understanding of the initial root causes and levels of acidification in
priori because determination of analytic solution involves a lot of assumptions making the results
unrealistic as opposed to the our numerical experiment approach which is cost effective and more
reliable results are obtained. Flow domain is assumed semi infinitely deep and homogeneous and it is subdivided into small units called control volumes of uniform dimension. A hybrid of Finite volume
and Finite difference methods are used to discretize space and time respectively in the governing
PDE. Discretized equations are inverted to obtain the concentrations at various nodes of the control
volumes by using mathematical codes developed in Mat-lab and the results presented using graphs
at different soil depths and time to determine the parameters that can help detect the contamination
levels before disastrous levels are reached and with ease.
From the results it is observed and concluded that the concentration levels of ions with depth and
time can easily be detected when diffusion coefficient and advection velocities are linearly
depended on time and mitigation strategies can easily be employed.