Groundwater flow equation, overview, derivation, and solution

Lhoussaine El Mezouary; Bouabid El Mansouri

doi:10.1051/e3sconf/202131404007

All issues

Volume 314 (2021)

E3S Web Conf., 314 (2021) 04007

References

Open Access

Issue		E3S Web Conf. Volume 314, 2021 The 6^th edition of the International Conference on GIS and Applied Computing for Water Resources (WMAD21)


Article Number		04007
Number of page(s)		4
Section		Geomatics, Remote Sensing and Modelling
DOI		https://doi.org/10.1051/e3sconf/202131404007
Published online		26 October 2021

Draoui, Y., et al., Quantification of Surface WaterGroundwater Exchanges by GIS Coupled with Experimental Gauging in an Alluvial Environment. [Google Scholar]
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El Mezouary, L., Modélisation mathématique et numérique des phénomènes d’écoulements et de transport de pollutions dans les milieux poreux: application a l’aquifère alluvial de la rivière de Magra, Italie. 2016. [Google Scholar]
El Mezouary, L., B. El Mansouri, and M. El Bouhaddioui. Groundwater forecasting using a numerical flow model coupled with machine learning model for synthetic time series. in Proceedings of the 4th Edition of International Conference on Geo-IT and Water Resources 2020, Geo-IT and Water Resources 2020. 2020. [Google Scholar]
El Mezouary, L., et al., Modélisation numérique de la variation saisonnière de la qualité des eaux souterraines de l’aquifère de Magra, Italie. 2015(2): p. 25-31. [Google Scholar]
El Mezouary, L., et al. Coupling of numerical flow model with the Susceptibility Index method (SI) to assess the groundwater vulnerability to pollution. in Proceedings of the 4th Edition of International Conference on Geo-IT and Water Resources 2020, Geo-IT and Water Resources 2020. 2020. [Google Scholar]
El Mezouary, L., et al., Stochastic modeling of flow in porous media by Monte Carlo simulation of permeability. 2016. 15. [Google Scholar]
Sadiki, M.L., et al., Improvement of groundwater resources potential by artificial recharge technique: a case study of charf el Akab aquifer in the Tangier region, Morocco. 2019. 7(3): p. 224-236. [Google Scholar]
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Meerschaert, M.M., C.J.J.O.C. Tadjeran, and A. Mathematics, Finite difference approximations for fractional advection–dispersion flow equations. 2004. 172(1): p. 65-77. [Google Scholar]
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[1] Draoui, Y., et al., Quantification of Surface WaterGroundwater Exchanges by GIS Coupled with Experimental Gauging in an Alluvial Environment. [Google Scholar]

[2] El Mansouri, B. and L.J.P.O.T.I.A.O.H.S. El Mezouary, Enhancement of groundwater potential by aquifer artificial recharge techniques: an adaptation to climate change. 2015. 366: p. 155-156. [Google Scholar]

[3] El Mezouary, L., Modélisation mathématique et numérique des phénomènes d’écoulements et de transport de pollutions dans les milieux poreux: application a l’aquifère alluvial de la rivière de Magra, Italie. 2016. [Google Scholar]

[4] El Mezouary, L., B. El Mansouri, and M. El Bouhaddioui. Groundwater forecasting using a numerical flow model coupled with machine learning model for synthetic time series. in Proceedings of the 4th Edition of International Conference on Geo-IT and Water Resources 2020, Geo-IT and Water Resources 2020. 2020. [Google Scholar]

[5] El Mezouary, L., et al., Modélisation numérique de la variation saisonnière de la qualité des eaux souterraines de l’aquifère de Magra, Italie. 2015(2): p. 25-31. [Google Scholar]

[6] El Mezouary, L., et al. Coupling of numerical flow model with the Susceptibility Index method (SI) to assess the groundwater vulnerability to pollution. in Proceedings of the 4th Edition of International Conference on Geo-IT and Water Resources 2020, Geo-IT and Water Resources 2020. 2020. [Google Scholar]

[7] El Mezouary, L., et al., Stochastic modeling of flow in porous media by Monte Carlo simulation of permeability. 2016. 15. [Google Scholar]

[8] Sadiki, M.L., et al., Improvement of groundwater resources potential by artificial recharge technique: a case study of charf el Akab aquifer in the Tangier region, Morocco. 2019. 7(3): p. 224-236. [Google Scholar]

[9] Liu, J.Z., L.D. Zhang, and G.H.J.B.J. Yue, Fractal dimension in human cerebellum measured by magnetic resonance imaging. 2003. 85(6): p. 4041-4046. [Google Scholar]

[10] Deng, W.J.J.O.C.P., Numerical algorithm for the time fractional Fokker–Planck equation. 2007. 227(2): p. 1510-1522. [Google Scholar]

[11] Zhang, Y.J.A.M. and Computation, A finite difference method for fractional partial differential equation. 2009. 215(2): p. 524-529. [Google Scholar]

[12] Yuste, S.B. and L.J.S.J.O.N.A. Acedo, An explicit finite difference method and a new von Neumanntype stability analysis for fractional diffusion equations. 2005. 42(5): p. 1862-1874. [Google Scholar]

[13] Podlubny, I., et al., Matrix approach to discrete fractional calculus II: partial fractional differential equations. 2009. 228(8): p. 3137-3153. [Google Scholar]

[14] Hanert, E.J.C. and Fluids, On the numerical solution of space–time fractional diffusion models. 2011. 46(1): p. 33-39. [Google Scholar]

[15] Lin, R., et al., Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation. 2009. 212(2): p. 435-445. [Google Scholar]

[16] Meerschaert, M.M., C.J.J.O.C. Tadjeran, and A. Mathematics, Finite difference approximations for fractional advection–dispersion flow equations. 2004. 172(1): p. 65-77. [Google Scholar]

[17] Crank, J. and P. Nicolson. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. in Mathematical Proceedings of the Cambridge Philosophical Society. 1947. Cambridge University Press. [Google Scholar]