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Ph.D.
(Science)
MATHEMATICAL MODELLING AND ANALYSIS OF
ONE DIMENSIONAL GROUNDWATER FLOW PROBLEMS

Ph.D. Scholar : Shah Krisha Dhirenkumar
Research Supervisor : Prof. (Dr.) Amit K. Parikh

Regi. No.: 17146061003
Abstract :
Recent research has placed a lot of emphasis on the fluid flow that happens under water.
Different physical phenomena of fluid flow arise below the ground Surface and in porous
media. When oil and water flowing simultaneously in porous medium in groundwater,
some physical phenomena occur. The mathematical formulation of these physical
phenomena leads to the non-linear partial differential equations. It is a challenging task to
solve nonlinear partial differential equation.

Some standard transformation like similarity transformation is used to transform
nonlinear partial differential equation into nonlinear ordinary differential equation but still
it is difficult to get its exact solution. Many researchers are working on approximate
solution of some nonlinear partial differential equation using different numerical
techniques. In present work our attempt is to obtain classical approximate solution of
nonlinear partial differential equation of many real-world problems.

The thesis discusses Mathematical models of Groundwater infiltration phenomena, with
external input and output, Groundwater recharge with linear and parabolic permeability,
Instability Phenomenon in homogenous and heterogeneous porous media and co-current
imbibition phenomenon in homogenous and heterogeneous porous media.

We have derived non-linear partial differential equations and we have solved those
equations are solved using differential transform method. In instability phenomenon in
homogenous and heterogeneous porous media we have studied and solved inclination in
small angles and vertical direction as well. In Co-current imbibition phenomenon in
homogenous and heterogeneous porous media we have studied and solved inclination in
small angles and vertical direction as well. MatLab software has been used to derive
graphical solution.

Key words: Groundwater Infiltration Phenomenon, Groundwater Recharge, Inclined
Instability phenomenon, Co-current Imbibition Phenomenon, homogeneous porous
media, Heterogeneous porous media, Differential Transform method, Oil recovery
process, Nonlinear source, Logarithmic source.

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