Model of conversion of flow from confined to unconfined with the generalized Mittag-Leffler process. (January 2023)

• Record Type: Journal Article
• Authors: Morakaladi, M.I.C.; Atangana, A.
• Is Part Of: Journal of African earth sciences. Volume 197(2023)
• Publication Date: 2023-01
• Subjects: Confined aquifer -- Unconfined aquifer -- Mittag-leffler function -- Atangana-baleanu fractional derivative -- Numerical scheme -- Stability analysis; Earth sciences -- Africa -- Periodicals; Earth sciences -- Middle East -- Periodicals; Geology -- Africa -- Periodicals; Geology -- Middle East -- Periodicals; Sciences de la terre -- Afrique -- Périodiques; Sciences de la terre -- Moyen-Orient -- Périodiques; Géologie -- Afrique -- Périodiques; Géologie -- Moyen-Orient -- Périodiques; Earth sciences; Geology; Africa; Middle East; Periodicals; Electronic journals; 556.05
• DOI: 10.1016/j.jafrearsci.2022.104753
• Languages: English
• ISSNs: 1464-343X

Abstract

Abstract: We considered in the paper a mathematical model used to replicate the conversion from confined to unconfined flow due to groundwater abstraction. We argued that the existing model, while very useful, however, does not capture the effect of the aquitard with fractures, as in such media there is a crossover behavior from stretched exponential to power law. We modified the model by replacing the exponential decay component with the generalized Mittag-Leffler function, which yields a model with nonlocal properties. To solve the system, we consider two different approaches, the first consists of discretizing the model directly using the forward Euler method, and the second consists of converting the model to an integral equation and deriving the solution by employing a polynomial interpolation approach. We presented using the Von Neumann stability approach for the confined part and both yield stability unconditionally. Some numerical simulations are performed. Highlights: Generalized-Mittag-Leffler function and distribution. Conversion from confined to unconfined flow. Numerical schemes. Laplace transform and related diagrams.