Abstract
Darcy’s law is the basic law of flow, and it produces a partial differential equation is similar to the heat transfer equation when coupled with an equation of continuity that explains the conservation of fluid mass during flow through a porous media. This article, titled the groundwater flow equation, covers the derivation of the groundwater flow equations in both the steady and transient states. We look at some of the most common approaches and methods for developing analytical or numerical solutions. The flaws and limits of these solutions in reproducing the behavior of water flow on the aquifer are also discussed in the article.
Highlights
Excessive exploitation of fresh water has raised demand for groundwater, prompting many academics to concentrate their efforts on understanding the phenomena of groundwater flow, and as a result, new research has focused on groundwater flow modeling [18]
Darcy's law is the basic law of flow, and it produces a partial differential equation is similar to the heat transfer equation when coupled with an equation of continuity that explains the conservation of fluid mass during flow through a porous media
We look at some of the most common approaches and methods for developing analytical or numerical solutions
Summary
Excessive exploitation of fresh water has raised demand for groundwater, prompting many academics to concentrate their efforts on understanding the phenomena of groundwater flow, and as a result, new research has focused on groundwater flow modeling [18]. The characteristics of the newly suggested fractional-order derivative allow it to simulate the flow of water in various levels or scales inside a geological structure known as an aquifer. There has been a lot of research on finite difference methods for constant-order time or space fractional diffusion equations [10, 11]. Chen et al developed an implicit difference approximation method for constant-order temporal fractional diffusion equations [12]. Podlubny et al developed the matrix method [14], while Hanert provided a flexible numerical system for the discretization of the space-time fractional diffusion problem [15]. Zhuang et al recently looked at numerical schemes for the VO space fractional advection-dispersion equation [16], while Lin et al looked at the explicit scheme for the VO nonlinear space fractional diffusion equation [17]
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