Boundary element method of modelling steady state groundwater flow

Abstract

Water is a very important resource for any living organism and is mainly underground. The movement of groundwater is governed by the Laplace equation ∇ 2 h = 0, where h is the hydraulic head. Much research has been on groundwater modelling and many of them are inspired by Darcy's law. The Boundary Element Method is one of the few widely used numerical techniques for solving boundary value problems in engineering and physical sciences. In this study, a steady state groundwater flow model has been analyzed using the boundary element method. The results show that water moves from points at higher hydraulic head to points at lower hydraulic head. This result using the boundary element method is in perfect agreement with the 2014 result by the same authors using the finite volume method.

A Pilot Fortran Software Library for the Solution of Laplace’s Equation by the Boundary Element Method

“…Laplace's equation therefore acts as a model problem for developing the BEM. Laplace's equation also has a number of applications; steady-state heat conduction, steady-state electric potential, gravitation and groundwater flow [4][5][6][7][8][9][10][11][12][13].…”

Mathematical Modeling of Transient and Steady-State Groundwater Flow in a Confined Aquifer

“…The general equation has several different forms depending on whether the flow is saturated or unsaturated, two-dimensional or three-dimensional, isotropic or anisotropic, and transient or steady state (Waghmare, 2016). According Nkurunziza et al (2014), one needs hydrological inputs, hydraulic parameters, and initial and boundary conditions for the calculations in groundwater modeling. Groundwater flow models simulate either steady or unsteady states (transient flow).…”