Systems Science and Applied Mathematics
Articles Information
Systems Science and Applied Mathematics, Vol.2, No.2, Apr. 2017, Pub. Date: Aug. 1, 2017
Kirchhoff Transformation of Richards Equation for Simulating Water Flow in Porous Media
Pages: 8-12 Views: 1338 Downloads: 1085
[01] Sabri Kanzari, National Research Institute for Rural Engineering, Water and Forestry, INRGREF, University of Carthage, Ariana, Tunisia.
[02] Sana Ben Mariem, National Research Institute for Rural Engineering, Water and Forestry, INRGREF, University of Carthage, Ariana, Tunisia.
A mathematical model that describes water flow through the unsaturated porous media is detailed in this paper. Indeed, this problem is based on the Richards equation. Resolution of such one-dimensional problem is performed using a Kirchhoff Transformation and a numerical approach based on the finite difference method.
Porous Media, Water Flow, Kirchhoff Transformation, Finite Difference Method
[01] Milnes E., and Perrochet P., 2005. Direct simulation of solute recycling in irrigated areas. Advances in water resoureces 29, 1140-1154.
[02] Petalas C. and Lambrakis N., 2006. Simulation of intense salinzation phenomena in coastal aquifers – the case of the coastal aquifers of Thrace. Journal of Hydrology 324, 51-64.
[03] Martos F. S. and Bosch A. P., 1999. Boron and the origin of salinzation in an aquifer in southeast Spain. Surface Geosciences 328, 751-757.
[04] Abu-Sharar T. M. and Salameh A. S., 1995. Reduction in hydraulic conductivity and infiltration rate in relation to aggregate stability and irrigation water turbidity. Agricultural Water Management 29, 53-62.
[05] Al-Senafy M. and Abraham J., 2004. Vulnerability of groundwater resources from agricultural activities in southern Kuwait. Agricultural Water Management 64, 15.
[06] Braudeau E., Mohtar R. H., Ghezal N. E., Crayol M., Salahat M., and Martin P., 2009. A multi-scale “soil water structure” model based on the pedostructure concept. Hydrol Earth Syst. Sci. Discuss., 6, 1111–1163.
[07] Kanzari S., Ben Mariem S. and Sahraoui H., 2016. A Reduced Differential Transform Method for Solving the Advection and the Heat-like Equations. Physics Journal, 2(2): 84-87.
[08] van Genuchten. M. T. and Simunek J., 2004. Integrated modeling of vadose zone flow and transport processes, in Unsaturated Zone Modelling: Progress. Challenges and Applications. Frontis Ser.. vol. 6. edited by R. A. Feddes. G. H. de Rooij. and J. C. van Dam, 37 – 69. Springer. New York.
[09] Suarez D. L. and Simunek J., 1997. UNSATCHEM: Unsaturated water and solute transport model with equilibrium and kinetic chemistry. Soil Sci. Soc, 1633–1646.
[10] Gonçalves M. C., Simunek J., Ramos TB., Martins J. C., Neves M. J., and Pires F. P., 2006. Multicomponent solute transport in soil lysimeters irrigated with waters of different quality. Water Resources Review., 42-17.
[11] Forkutsa I., Sommer R., Shirokova Y. P., Lamers J. P. A., Kienzler K., Tischbein C., Martius P. L. and Vlek G., 2009. Modeling irrigated cotton with shallow groundwater in the Aral Sea Basin of Uzbekistan: II. Soil salinity dynamics. Irri Sci, 27, 319-330.
[12] Mualem, Y., 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12(3), 513-522.
[13] Haverkamp R., Vauclin M., Touma J., Wierenga J. and Vachaud G., 1977. A comparison of numerical simulation models for one-dimensional infiltration. Soil Science Society American Journal, 41: 285-294.
[14] J. S. Pérez Guerrero, E. M. Pontedeiro, M. Th. van Genuchten, T. H. Skaggs, “Analytical solutions of the one-dimensional advection–dispersion solute transport equation subject to time-dependent boundary conditions”, Chemical Engineering Journal, Volume 221, 1 April 2013, pp. 487-491.
[15] Yunwu Xiong, Guanhua Huang, Quanzhong Huang, “Modeling solute transport in one-dimensional homogeneous and heterogeneous soil columns with continuous time random walk”, Journal of Contaminant Hydrology, Volume 86, Issues 3–4, 10 August 2006, pp. 163-175.
[16] A. Ghafoor, J. Koestel, M. Larsbo, J. Moeys, N. Jarvis, “Soil properties and susceptibility to preferential solute transport in tilled topsoil at the catchment scale”, Journal of Hydrology, Volume 492, 7 June 2013, pp. 190-199.
[17] F. San Jose Martinez, Y. A. Pachepsky, W. J. Rawls, “Modelling solute transport in soil columns using advective–dispersive equations with fractional spatial derivatives”, Advances in Engineering Software, Volume 41, Issue 1, January 2010, pp. 4-8.
[18] C. Guan, H. J. Xie, Y. Z. Wang, Y. M. Chen, Y. S. Jiang, X. W. Tang, “An analytical model for solute transport through a GCL-based two-layered liner considering biodegradation, Science of The Total Environment”, Volumes 466–467, 1 January 2014, pp. 221-231.
[19] S. C. Lessoff, P. Indelman, “Analytical model of solute transport by unsteady unsaturated gravitational infiltration”, Journal of Contaminant Hydrology, Volume 72, Issues 1–4, August 2004, pp. 85-107.
[20] Alaa El-Sadek, “Comparison between numerical and analytical solution of solute transport models”, Journal of African Earth Sciences, Volume 55, Issues 1–2, September 2009, pp. 63-68.
[21] D. Hilhorst, C. Jouron, Y. Kelanemar, “Coupled heat and mass transfer in porous media”. Actes des journées numériques " Computational methods for transport in porous media". Besançon, 1994.
[22] Kanzari S. and Ben Mariem S., 2014. One-dimensional numerical modeling for water flow and solute transport in an unsaturated soil. International Journal of Applied Science and Mathematics, 1(2): 52-56.
[23] Berninger H., 2007. Domain Decomposition Methods for Elliptic Problems with Jumping Nonlinearities and Application to the Richards Equation. PhD thesis Freie Universit ̈at Berlin.
[24] Richards LA., 1931. Capillary conduction of liquids through porous mediums. Journal of Applied Physics, 1: 318-333.
[25] Philip J. R., 1957. The theory of infiltration, 1-7. Soil Science, 83-85.
[26] Haverkamp R., Vauclin M., Touma J., Wierenga J. and Vachaud G., 1977. A comparison of numerical simulation models for one-dimensional infiltration. Soil Science Society American Journal, 41: 285-294.
[27] Simunek J., Huang K., Sejna M. and van Genuchten M. T., 2005. The HYDRUS-1D software package for simulating the one-dimensional movement of water. heat. and multiple solutes in variably - saturated media. Internaional ground water modelling center Colorado School of Mines. Golden. Colorado, 162 p.
MA 02210, USA
AIS is an academia-oriented and non-commercial institute aiming at providing users with a way to quickly and easily get the academic and scientific information.
Copyright © 2014 - American Institute of Science except certain content provided by third parties.