Solving two-dimensional groundwater flow equation using alternating direction implicit method

Abstract

Groundwater model can be described as a mathematical model and the equation of groundwater is governed by partial differential equation. In order to solve the groundwater flow equation, numerical method such that Finite Difference Method (FDM) is used. In this research, a two-dimensional transient groundwater flow equation for a confined, nonleaky, and homogeneous with mixed boundary conditions is solved using Alternating Direction Implicit (ADI) method where ADI method is one of the FDM. The algorithm of ADI method has been developed for three different types of boundary conditions that is Dirichlet condition, Neuman condition and Mixed condition. The transient groundwater flow equation has been derived and was solved using ADI method by Matlab software. Then, the results obtained were compared to analytical solution. Since the solutions from numerical method provide the small error when compared to the analytical solutions, it therefore can be concluded that ADI method provides good approximations in solving two-dimensional groundwater transient flow problem.