mathematical modelling and analysis of one dimensional groundwater flow problems

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. newlineSome 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. newlineThe 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. newlineWe 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. newline newline