Finite Volume Method of Modelling Transient Groundwater Flow

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.

Boundary element method of modelling steady state groundwater flow

“…The following discussion revealed that water flows from points at higher hydraulic head to points with lower hydraulic head which is in agreement with the general theory of groundwater flow and also with the results obtained in our 2014 paper [8].…”

“…We now show how equation (41) may be applied to obtain a simple boundary element procedure for solving numerically the interior boundary value problem defined by equations (6), (7) and (8). The advantage of the BEM is to discretize the boundary into finite number of segments, not necessarily equal, which are called boundary elements or elements.…”

“…Equation 3includes the storage term (S s ∂h ∂t ) which occurs only in transient flow when ∂h ∂t = 0 [8]. If however, the flow is steady state, ∂h ∂t = 0, the righthand-side of (3) become zero.…”