Abstract:
A one dimensional mass transport equation whose solution is ill-posed is considered
to model flow of solutes in porous medium. The diffusion coefficient and advection
velocity in the governing partial differential equation (PDE) are first taken constant
and secondly linearly time dependent and not proportional to each other. Flow
domain is assumed semi infinitely deep and homogeneous and it is subdivided into
small units called control volumes of uniform dimension. 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. It is observed 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.
