Differential Quadrature Solution for One-Dimensional Aquifer Flow

Birol Kaya,Yalcin Arisoy

doi:10.3390/mca16020524

Abstract

Differential Quadrature Method (DQM) has been applied to the solution of aquifer flow problems. Three examples from of each of the three one-dimensional aquifer flow equation problems, a confined aquifer flow with time dependent boundary conditions, a composite confined aquifer and an unconfined aquifer with seepage, were examined. The results of DQM solution were then compared with the results obtained from analytical solution, the Explicit Finite Differences Method and Implicit Finite Differences Method. Based on the comparison results, it was concluded that the DQM provides similar results but with relatively faster calculation speed, less nodes and memory usage.

Highlights

The one-dimensional unsteady flow equation for groundwater flow is a parabolic differential equation, and typically, Finite Differences Methods (FDM) and Finite Elements Method (FEM) are used for the numerical solution
Differential Quadrature Method (DQM) has found increasing use in recent years in Hydraulic Engineering, because it is an alternative approach to the conservative methods
From the previous applications of DQM, it is seen that the results of DQM are converged rapidly and closer to analytical solutions than other numerical solutions [12]

Summary

INTRODUCTION

The one-dimensional unsteady flow equation for groundwater flow is a parabolic differential equation, and typically, Finite Differences Methods (FDM) and Finite Elements Method (FEM) are used for the numerical solution. Wang and Anderson [32] have studied several groundwater flow problems, in a finite aquifer with recharge boundary, by using an explicit finite difference method for numerical solution. Onder [22] has found an analytical solution for one of the problems that Wang and Anderson had, by examining the flow resulting from a sudden rise or decline in the water stage of a flood channel in a composite aquifer. As “the case (1)”, this problem was examined in the present study. Butter and Liu [6] have presented a semi-analytical solution for the analysis of drawdown data obtained from pump test performed in non-uniform aquifers, which represent a linear strip case. As the last numerical example, surface and groundwater interact in an unconfined aquifer is “the case (3)” in this present study. A comparison, between these FEM solutions and DQM solutions that were obtained from the examples examined in the present study, was performed

DIFERENTIAL QUADRATURE METHOD

DQM IN GROUNDWATER FLOW APPLICATIONS

NUMERICAL SOLUTIONS

CONCLUSION