Articles | Volume 21, issue 3
Hydrol. Earth Syst. Sci., 21, 1547–1557, 2017
https://doi.org/10.5194/hess-21-1547-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Special issue: Modeling hydrological processes and changes
Hydrol. Earth Syst. Sci., 21, 1547–1557, 2017
https://doi.org/10.5194/hess-21-1547-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
13 Mar 2017
Research article
| 13 Mar 2017
Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time
M. Levent Kavvas et al.
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Cited
14 citations as recorded by crossref.
- Using a shifted Grünwald‐Letnikov scheme for the Caputo derivative to study anomalous solute transport in porous medium P. Mascarenhas et al. 10.1002/nag.2936
- Modelling solute dispersion in periodic heterogeneous porous media: Model benchmarking against intermediate scale experiments S. Majdalani et al. 10.1016/j.jhydrol.2018.03.024
- Numerical Evaluation of Fractional Vertical Soil Water Flow Equations A. Ercan & M. Kavvas 10.3390/w13040511
- Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time M. Kavvas et al. 10.5194/esd-11-1-2020
- Stochastic Foundation to Solving Transient Unsaturated Flow Problems Using a Fractional Dispersion Term P. Mascarenhas & A. Cavalcante 10.1061/(ASCE)GM.1943-5622.0002251
- Fractional derivative approach to non-Darcian flow in porous media H. Zhou & S. Yang 10.1016/j.jhydrol.2018.09.039
- A fractional derivative perspective on transient pulse test for determining the permeability of rocks S. Yang et al. 10.1016/j.ijrmms.2018.11.013
- Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time M. Kavvas et al. 10.5194/esd-8-921-2017
- Numerical simulation of irrigation scheduling using fractional Richards equation M. Romashchenko et al. 10.1007/s00271-021-00725-3
- A fast finite-difference algorithm for solving space-fractional filtration equation with a generalised Caputo derivative V. Bohaienko 10.1007/s40314-019-0878-5
- Identification of fractional water transport model with ψ-Caputo derivatives using particle swarm optimization algorithm V. Bohaienko et al. 10.1016/j.amc.2020.125665
- Time-space fractional governing equations of one-dimensional unsteady open channel flow process: Numerical solution and exploration A. Ercan & M. Kavvas 10.1002/hyp.11240
- Time-space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation T. Tu et al. 10.1002/hyp.11500
- Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique V. Bohaienko 10.1016/j.rico.2021.100068
14 citations as recorded by crossref.
- Using a shifted Grünwald‐Letnikov scheme for the Caputo derivative to study anomalous solute transport in porous medium P. Mascarenhas et al. 10.1002/nag.2936
- Modelling solute dispersion in periodic heterogeneous porous media: Model benchmarking against intermediate scale experiments S. Majdalani et al. 10.1016/j.jhydrol.2018.03.024
- Numerical Evaluation of Fractional Vertical Soil Water Flow Equations A. Ercan & M. Kavvas 10.3390/w13040511
- Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time M. Kavvas et al. 10.5194/esd-11-1-2020
- Stochastic Foundation to Solving Transient Unsaturated Flow Problems Using a Fractional Dispersion Term P. Mascarenhas & A. Cavalcante 10.1061/(ASCE)GM.1943-5622.0002251
- Fractional derivative approach to non-Darcian flow in porous media H. Zhou & S. Yang 10.1016/j.jhydrol.2018.09.039
- A fractional derivative perspective on transient pulse test for determining the permeability of rocks S. Yang et al. 10.1016/j.ijrmms.2018.11.013
- Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time M. Kavvas et al. 10.5194/esd-8-921-2017
- Numerical simulation of irrigation scheduling using fractional Richards equation M. Romashchenko et al. 10.1007/s00271-021-00725-3
- A fast finite-difference algorithm for solving space-fractional filtration equation with a generalised Caputo derivative V. Bohaienko 10.1007/s40314-019-0878-5
- Identification of fractional water transport model with ψ-Caputo derivatives using particle swarm optimization algorithm V. Bohaienko et al. 10.1016/j.amc.2020.125665
- Time-space fractional governing equations of one-dimensional unsteady open channel flow process: Numerical solution and exploration A. Ercan & M. Kavvas 10.1002/hyp.11240
- Time-space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation T. Tu et al. 10.1002/hyp.11500
- Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique V. Bohaienko 10.1016/j.rico.2021.100068
Latest update: 08 Aug 2022
Short summary
In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. By the introduction of the Brooks–Corey constitutive relationships, an explicit form of the equations is obtained. The developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations.
In this study dimensionally consistent governing equations of continuity and motion for...
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