Mathematical Modelling of Surface Water-groundwater Flow Mechanism: A Review of Conceptual Evolution

Abstract

Surface-groundwater interaction is an important research area because of its function in wastewater treatment, irrigation, drainage, flood management, erosion control, and sediment control. Under a range of hydrological situations, mathematical models are frequently employed to estimate surface-groundwater interactions. The study of groundwater is cost affected. To carry out constructed wetland study and cleaning up of contaminated water on the land surface is very costly. This gave birth to hydrology modelling. Due to their cost effectiveness and ability to accommodate variations in aquifer parameters, mathematical models have gained immense importance in the past few decades. In order to analyse exchange of water between aquifer, atmosphere and surface water, one of important essential components is to understand groundwater movement theory. The goal of this review paper is to highlight the contributions of hydrologists from around the world to the growing field of surface-ground water interaction, who designed, studied, executed, and validated the established mathematical models. To begin, we will briefly discuss the key mathematical equations that govern groundwater flow in both unconfined and  confined aquifer systems. The evolution of stream-aquifer models is provided in chronological order to enable a clear understanding of previous research' contributions. Without delving into mathematical intricacies, the methodology employed in previous work is adequately presented. It also summarizes current developments in groundwater flow in the context of vertical streambed, partial penetration, stream-stage changes, and numerous recharge/discharge basins.