Journal of Mathematics and Statistics 10 (1): 92-110, 2014 ISSN: 1549-3644 © 2014 Science Publications doi:10.3844/jmssp.2014.92.110 Published Online 10 (1) 2014 (http://www.thescipub.com/jmss.toc) Corresponding Author: J.M. Mango, Department of Mathematics, College of Natural Sciences, Makerere University, Kampala, Uganda 92 Science Publications JMSS FINITE VOLUME METHOD OF MODELLING TRANSIENT GROUNDWATER FLOW Muyinda, N., G. Kakuba and J.M. Mango Department of Mathematics, College of Natural Sciences, Makerere University, Kampala, Uganda Received 2014-01-08; Revised 2014-01-29; Accepted 2014-02-15 ABSTRACT In the field of computational fluid dynamics, the finite volume method is dominant over other numerical techniques like the finite difference and finite element methods because the underlying physical quantities are conserved at the discrete level. In the present study, the finite volume method is used to solve an isotropic transient groundwater flow model to obtain hydraulic heads and flow through an aquifer. The objective is to discuss the theory of finite volume method and its applications in groundwater flow modelling. To achieve this, an orthogonal grid with quadrilateral control volumes has been used to simulate the model using mixed boundary conditions from Bwaise III, a Kampala Surburb. Results show that flow occurs from regions of high hydraulic head to regions of low hydraulic head until a steady head value is achieved. Keywords: Groundwater Flow, Finite Volume Method, Mathematical Modelling, Discretization 1. INTRODUCTION The groundwater resources of the earth have for a long time been subjected to degradation as a result of man’s increasing utilization of natural resources and worldwide industrialization. Beginning in the 1960s, contaminated aquifers were cleaned up and protected from further degradation in various countries around the world because government agencies identified groundwater as a valuable and increasingly important water resource (Batu, 2005). During this time, it was found that mathematical groundwater flow and solute transport modelling could be used as an efficient and cost-effective tool in the investigation and management of groundwater resources. Since then, mathematical models of groundwater flow have been widely used for a variety of purposes ranging from water supply studies to designing contaminant cleanup. The availability of computers and the development of efficient computer programs to do the computations involved in the models have also led to an increase in the use of numerical mathematical models in the analysis of groundwater flow and contaminant transport problems. Mathematical models are conceptual descriptions or approximations that describe the physical system using mathematical equations. They based on solving an equation (or a system of equations) that describe the physical phenomenon. Such equations are called governing equations of the specified phenomenon. For groundwater flow, the governing equations are Darcy’s law and the principle of mass balance (conservation). Darcy’s law is an equation that describes the flow of a fluid through a porous medium. The law was formulated in 1856 by French engineer Henry Darcy while working on a project involving the use of sand to filter the water supply for the city of Dijon in France. From his experiments (Fitts, 2012; Freeze, 1994), Darcy observed that the rate of flow through a homogeneous sand column of constant cross-sectional area was proportional to both the cross-sectional area of the column and the defference in water level elevations at the inflow and outflow reservoirs of the column and inversely proportional to the length of the column. This equation is usually written as Equation (1) (Bear and Cheng, 2010): s dh q K ds =- (1) Where: q s = The flow per unit cross-sectional area in direction s, K = The hydraulic conductivity and