| dc.description.abstract | Advecrion-diffusion equation arises from modeling of physical processes in a wide range of scientific disciplines.The (3+1) dimensional Advection-Diffusion equation we derived can generally be written as;
= ;! r, y. c. t)Cxx+ h(x, y, z , t)Cyy+ h(x, y, z , t)Czz+ J,(x, y, z, t)Cxy+ f5(x, y, z, t)Cx+ f6(X, y, z. t)Cy•
.c,•,.n:on terms Cx and Cy describe how water is carried along an underground layer of water•
-; permeable rock called aquifer due to bulk fluid motion. The diffusion terms Cxx, Cyy, C,, and
C describe the spreading of contaminant due to random molecular collision and Ct defines the rate of
=e of concentration with respect to time. (l+l) ADE was derived and solved to investigate water
•: but the results could not be put to comprehensive physical interpretation in the absence of a
ll>,•--�• and a vertical dimension. (2+1) ADE was also derived and solved to investigate contaminant
a,ac,...:ca1:on in aquifer but the results again could not be subjected to physical interpretation because
.uriou was iu series forni.the advection and diffusion parameters were arbitrarily assigned and
e:fect of diffusion on the vertical plane could not be ascertained. It was therefore important to
_. -., and solve the (3+ 1) ADE with a mixed derivative to investigate the effect of varying exponential decaying Advection-Diffusion parameters on contaminant concentration in aquifer. The model
,;.,n that governs the change of concentration with respect to time is solved numerically by Finite
=�..re::oce Method using 111ATLAB computer software programme. An Alternating Direction Explicit
..\.'.ternating Direction Implicit numerical schemes for the equations are developed and the concepts
• C "-' ency and Stability discussed and analysed. The study found out that both numerical schemes
:JS. tent with the model equation, implying that the model equation could be recovered from the gebraic equations of the schemes developed. Von Neuman method is used to analyse the Sta•
, .he numerical schemes developed and the two schemes are found to be unconditionally stable.
�--!.ltion for the model equation indicate that contaminant concentration increases with respect
c,ne in both schemes when the diffusion parameters are exponential and the advection parameters oecaying. On the other hand, contaminant concentration decreases with respect to time in both """"'""" when the diffusion parameter is decaying and the advection parameter is exponential. This
_ ,_ a big contribution to mathematical knowledge to the extent that the results obtained will
-- in rhe identification of suitable underground water sources drilling sites.complement the current
-.JCal Electrical Sounding technology which addresses the question of quantity and not quality of
="""-•=ound water and to reduce considerably the cost of water prospecting | en_US |
