Numerical modeling of groundwater flow based on explicit and fully implicit schemes of finite volume method

Abstract

This paper documents a novel numerical model for calculating the behavior of unsteady, one-dimensional groundwater flow by using the finite volume method. The developed model determined water table fluctuations for different scenarios as follows: Drainage and recession from an unconfined aquifer, and water table fluctuations above an inclined leaky layer due to ditch recharge with a constant and variable upper boundary condition. The Boussinesq equation, which is the governing equation in this domain, is linearized and solved numerically in both of the explicit and fully implicit conditions. Meanwhile, the upwind scheme is employed to discretize the governing equation. The computed outcomes of both the explicit and implicit approaches agreed well with the results of analytical solution and laboratory experiments. The main reason is that in the first half of simulation process explicit scheme obtains slightly better results and in the second half of the simulation process fully implicit scheme predicts more reliable outcomes that are hidden in the neighbor node points. As a final point, the numerical outcomes confirm that the developed model is capable of calculating satisfactory outcomes in engineering and science applications.

Analytical Solution of Vertically Integrated Equations of a Confined Aquifer in two-dimension using Finite Volume method

“…[13] presented a model of groundwater dynamics under stationary flow and solved the developed mathematical model using the Finite Difference Method, and an application on the specific study area of the Ayamonte-Huelva aquifer in Spain was performed. [5] developed a novel numerical model in order to calculate the behavior of unsteady, one-dimensional groundwater flow using the finite volume method. Various scenarios for drainage and recession from an unconfined aquifer, as well as water table fluctuations above an inclined leaky layer due to ditch recharge with a constant and variable upper boundary condition, were performed.…”

A Numerical Model with Finite Difference Schemes for Multi-Species Solute Transport in Porous Media

“…To manage surface-and ground-water resources, estimating the contaminant and solute transport phenomenon is significant. Some researchers have conducted experimental studies or developed numerical methods for groundwater problems (Kaya and Arisoy 2011; e e 2016; Dalkiliç and Gharehbaghi 2021). However, there are benefits in considering the phenomenon of pollutant and solute transport when examining groundwater problems.…”