This book provides comprehensive analysis of a number of groundwater issues, ranging from flow to pollution problems. Several scenarios are considered throughout, including flow in leaky, unconfined, and confined geological formations, crossover flow behavior from confined to confined, to semi-confined to unconfined and groundwater pollution in dual media. Several mathematical concepts are employed to include into the mathematical models’ complexities of the geological formation, including classical differential operators, fractional derivatives and integral operators, fractal mapping, randomness, piecewise differential, and integral operators. It suggests several new and modified models to better predict anomalous behaviours of the flow and movement of pollution within complex geological formations. Numerous mathematical techniques are employed to ensure that all suggested models are well-suited, and different techniques including analytical methods and numerical methods are used to derive exact and numerical solutions of different groundwater models.
- Includes modified numerical and analytical methods for solving new and modified models for groundwater flow and transport
- Presents new flow and transform models for groundwater transport in complex geological formations
- Examines fractal and crossover behaviors and their mathematical formulations
Mathematical Analysis of Groundwater Flow Models serves as a valuable resource for graduate and PhD students as well as researchers working within the field of groundwater modeling.
Table of Contents
Chapter 1. Analysis of the existing model for the vertical flow of groundwater in saturated-unsaturated zone. Chapter 2. New model of the saturated-unsaturated groundwater flow with power law and scale-invariant mean square displacement. Chapter 3. New model of the 1-D unsaturated-saturated groundwater flow with crossover from usual to confined flow mean square displacement. Chapter 4. A new model of the 1-D unsaturated-saturated groundwater flow with crossover from usual to sub-flow mean square displacement. Chapter 5. New model of the 1-D saturated-unsaturated groundwater flow using the fractal fractional derivative. Chapter 6. Application of the fractional-stochastic approach to saturated-unsaturated zone model. Chapter 7. Transfer function of the Sumudu, Laplace transforms and their application to groundwater. Chapter 8. Analyzing the new generalized equation of groundwater flowing within a leaky aquifer using power law, exponential decay law and mittag-leffler law. Chapter 9. Application of the new numerical method with caputo fractal-fractional derivative on the self-similar leaky aquifer equations. Chapter 10. Application of the new numerical method with caputo-fabrizio fractal-fractional derivative on the self-similar leaky aquifer equations. Chapter 11. Application of the new numerical method with atangana-baleanu fractal-fractional derivative on the self-similar leaky aquifer equations. Chapter 12. Analysis of general groundwater flow equation within a confined aquifer using Caputo fractional derivative and Caputo-Fabrizio fractional derivative. Chapter 13. Analysis of general groundwater flow equation with fractal derivative. Chapter 14. Analysis of general groundwater flow equation with fractal-fractional differential operators. Chapter 15. A new model for groundwater contamination transport in dual media. Chapter 16. Groundwater contamination transport model with fading memory property. Chapter 17. A new groundwater transport in dual media with power law process. Chapter 18. New groundwater transport in dual media with the Atangana-Baleanu differential operators. Chapter 19. Modelling Soil Moisture flow: New proposed models. Chapter 20. Deterministic and stochastic analysis of groundwater in unconfined aquifer model. Chapter 21. A New Method for Modeling Groundwater Flow Problems: Fractional-Stochastic Modeling. Chapter 22. Modelling a Conversion of a Confined to an Unconfined Aquifer Flow. Chapter 23. New Model to Capture the Conversion of Flow from Confined to Unconfined. Chapter 24. Modeling the diffusion of chemical contamination in soil with non-conventional differential operators. Chapter 25. Modelling groundwater flow in a confined aquifer with dual layers. Chapter 26. The dual Porosity Model. Chapter 27. One-Dimensional Modeling of Reactive Pollutant Transport in Groundwater: The Case of Two Species. Chapter 28. Stochastic modeling in confined and leaky aquifers.
Abdon Atangana is working at the Institute for Groundwater Studies, University of the Free State as a full Professor. His research interests are but not limited to fractional calculus and applications, numerical and analytical methods, modeling. He is author of more than 250 research papers and four books in top tier journals of applied mathematics and groundwater modeling. He was elected highly cited mathematicians 2019 and highly cited mathematicians with Crossfield impact 2020. He is a recipient of the World Academia of Science Award of mathematics 2020. He serves as editor in top tier journals in various fields of studies.