Mathematical model for conversion of groundwater flow from confined to unconfined aquifers with power law processes

Abstract

In this work, we propose a mathematical model to depict the conversion of groundwater flow from confined to unconfined aquifers. The conversion problem occurs due to the heavy pumping of confined aquifers over time, which later leads to the depletion of an aquifer system. The phenomenon is an interesting one, hence several models have been developed and used to capture the process. However, one can point out that the model has limitations of its own, as it cannot capture the effect of fractures that exist in the aquitard. Therefore, we suggest a mathematical model where the classical differential operator that is based on the rate of change is substituted by a non-conventional one including the differential operator that can represent processes following the power law to capture the memory effect. Moreover, we revise the properties of the aquitard to evaluate and capture the behaviors of flow during the process in a different aquitard setting. Numerical analysis was performed on the new mathematical models and numerical solutions were obtained, as well as simulations for various fractional order values.

Stability and numerical analysis via non-standard finite difference scheme of a nonlinear classical and fractional order model

“…Additionally, various models involving concepts of mathematical analysis have been utilized very well. In this regards we refer some work, where various analysis and numerical scheme have been used to study different kinds of problems as [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] , [50] .…”

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

“…The findings show that GW-PINN has a significant capacity for capturing the hydraulic head change for both confined and unconfined aquifers. [10] proposed a mathematical model to represent the transition of groundwater flow from confined to unconfined aquifers, specifically the classical differential operator that is based on the rate of change is replaced by a non-conventional one including the differential operator that can represent processes following the power law to capture the memory effect, after which the numerical analysis was carried out using the Caputo fractional operator, and numerical solutions were obtained. [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.…”