Numerical Simulation of Two-Dimensional Unsaturated Flow from a Trickle Irrigation Source Using the Finite-Volume Method
Publication: Journal of Irrigation and Drainage Engineering
Volume 141, Issue 4
Abstract
A numerical two-dimensional finite-volume model is developed to predict the moisture-based form of the Richard’s equation that describes the transient flow of water through homogeneous and heterogeneous unsaturated porous media from a trickle irrigation source in a cylindrical flow region. Clay loam soil is selected to represent the homogeneous porous media. This cylindrical flow domain of clay loam soil is initially at uniform volumetric water content. Numerical runs were conducted with a clay loam soil at water application rates from the trickle irrigation source at a small circular pond area. An assessment of the fully implicit and explicit time schemes and arithmetic and geometric mean weighing formulas are evaluated. A good agreement is obtained when comparing the experimental measured positions of the wetting front advance with the predicted results. In general, for numerical modeling of the unsaturated flow equation, the fully implicit time scheme with geometric mean weighing formula for estimating the approximate value of the nonlinear soil water diffusivity and hydraulic conductivity at the interface between adjacent control volumes can be recommended when the theta-based form of the Richard’s equation is solved. The predicted results show that the finite-volume method is mass conservative, and it is a recommended method for solving Richard’s equation.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The author would like to thank Dr. Mishaal Abdulameer Abdulkareem for his infinite support and cooperation throughout this study.
References
Abid, M. B. (2006). “Analytical solution of unsaturated soil water flow from a point source.” Ph.D. thesis, Dept. of Water Resources Engineering, College of Engineering, Baghdad Univ., Iraq.
Abid, M. B. (2012). “Numerical simulation of unsaturated flow in porous media using the finite volume method.” 1st National Conf. for Engineering Science FNCES’12, Al-Nahrain Univ., Baghdad, Iraq, 36–43.
Abid, M. B., Hamad, S. N., and Hussain, S. M. (2012). “Analytical solution of unsaturated soil water flow from a point source.” J. Eng., 18(1), 95–106.
Angelakis, A. N. (1977). “Time-dependent soil-water distribution in a two-dimensional profile of clay loam soil under a circular trickle source.” M.S. thesis, Univ. of California, Davis, CA.
Angelakis, A. N., Kadir, T. N., and Rolston, D. E. (1993a). “Time-dependent soil-water distribution under a circular trickle source.” Water Resour. Manage., 7(3), 225–235.
Angelakis, A. N., Rolston, D. E., Kadir, T. N., and Scott, V. H. (1993b). “Soil-water distribution under trickle source.” J. Irrig. Drain. Eng., 484–500.
Ben-Asher, J., Lomen, D. O., and Warrick, A. W. (1978). “Linear and nonlinear models of infiltration from a point source.” Soil Sci. Soc. Am. J., 42(1), 3–6.
Bhatnagar, P. R., and Chauhan, H. S. (2008). “Soil water movement under a single surface trickle source.” Agric. Water Manage., 95(7), 799–808.
Brandt, A., Bresler, E., Diner, N., Ben-Asher, I., Heller, J., and Goldberg, D. (1971). “Infiltration from a trickle source: I. Mathematical models.” Soil Sci. Soc. Am. Proc., 35(5), 675–682.
Celia, M. A., Bouloutas, B. T., and Zarba, R. L. (1990). “A general mass conservative solution for unsaturated flow equation.” Water Resour. Res., 26(7), 1483–1496.
Chung, S.-O. (1987). “Simulation of three-dimensional infiltration from a point source.” Proc., Int. Conf. on Infiltration Development and Application, Iowa Agriculture and Home Economics Experiment Station, Ames, IA, 114–123.
Clothier, B. E., and Scotter, D. R. (1982). “Constant-flux infiltration from a hemispherical cavity.” Soil Sci. Soc. Am. J., 46(4), 696–700.
Clothier, B. E., Scotter, D. R., and Harper, E. (1985). “Three-dimensional infiltration and trickle irrigation.” Trans. Am. Soc. Agric. Eng., 28(2), 497–501.
Elmaloglou, S., and Grigorakis, G. (1997). “Linear and nonlinear models of infiltration from surface line source of trickle irrigation.” ICID J., 46(2), 81–92.
Hariprasad, K. S., Kumar, M. S. M., and Sekhar, M. (2001). “Modeling flow through unsaturated zones: Sensitivity to unsaturated soil properties.” Sādhanā, 26(6), 517–528.
Haverkamp, R., and Vauclin, M. (1979). “A note on estimating finite difference interblock hydraulic conductivity values for transient unsaturated flow problems.” Water Resour. Res., 15(1), 181–187.
Healy, R. W., and Warrick, A. W. (1988). “A generalized solution to infiltration from a surface point source.” Soil Sci. Soc. Am. J., 52(5), 1245–1251.
Kirkham, D., and Powers, W. L. (1972). Advanced soil physics, Wiley-Interscience, New York.
Lockington, D., Parlange, J.-Y., and Surin, A. (1984). “Optimal prediction of saturation and wetting fronts during trickle irrigation.” Soil Sci. Soc. Am. J., 48(3), 493–494.
Lu, Z., and Zhany, D. (2004). “Analytical solution to steady state unsaturated flow in layered randomly heterogeneous soils via Kirchhoff transformation.” Adv. Water Resour., 27(8), 775–784.
Menziani, M., Pugnaghi, S., and Vincenzi, S. (2007). “Analytical solution of the linearized Richards equation for discrete arbitrary initial and boundary condition.” J. Hydrol., 332(1–2), 214–225.
Moncef, H., Hedi, D., Jelloul, B., and Mohamed, M. (2002). “Approach for predicting the wetting front depth beneath a surface point source: Theory and numerical aspect.” Irrig. Drain., 51(4), 347–360.
Parlange, J-Y. (1971). “Theory of water movement in soils: 2. One-dimensional infiltration.” Soil Sci., 111(3), 170–174.
Philip, J. R. (1968). “Steady infiltration from buried point sources and spherical cavities.” Water Resour. Res., 4(5), 1039–1047.
Philip, J. R. (1969). “Theory of infiltration.” Adv. Hydro Sci., 5, 215–296.
Pour, M. A., Shoshtari, M. M., and Adib, A. (2011). “Numerical solution of Richards equation by using of finite volume method.” World Appl. Sci. J., 14(12), 1838–1842.
Raats, P. A. (1971). “Steady infiltration from point sources, cavities and basins.” Soil Sci. Soc. Am. Proc., 35(5), 689–694.
Rubin, J. (1968). “Theoretical analysis of two-dimensional, transient flow of water in unsaturated and partly saturated soils.” Soil Sci. Soc. Am. Proc., 32(5), 607–615.
Shahraiyni, H. T., and Ataie Ashtiani, B. (2012). “Mathematical forms and numerical schemes for the solution of unsaturated flow equations.” J. Irrig. Drain. Eng., 63–72.
Srivastava, R., and Yeh, T. C. J. (1999). “Analytical solution for one-dimensional transient infiltration toward the water table in homogeneous and layered soils.” Water Resour. Res., 27(5), 753–762.
Taghavi, S. A., Marino, M. A., and Rolston, D. E. (1984). “Infiltration from a trickle source.” J. Irrig. Drain. Eng., 331–341.
Taghavi, S. A., Marino, M. A., and Rolston, D. E. (1985). “Infiltration from a trickle source in a heterogeneous soil medium.” J. Hydrol., 78(1–2), 107–121.
Van Genuchten, M. T. (1978a). “Calculating the unsaturated hydraulic conductivity with a new closed form analytical model.”, Water Resource Program, Dept. Civil Engineering, Princeton Univ., Princeton, NJ.
Van Genuchten, M. T. (1978b). “Numerical solution of the one-dimensional saturated-unsaturated flow equation.”, Water Resource Program, Dept. Civil Eng., Princeton Univ., Princeton, NJ.
Vasconcellos, C. A. B., and Amorim, J. C. C. (2001). “Numerical simulation of unsaturated flow in porous media using a mass-conservative model.” Proc., COBEM, 16th Brazilian Congress of Mechanical Engineering, Fluid Mechanics, Brazil, Vol. 8, 139–148.
Versteeg, H. K., and Malalasekera, W. (1995). An introduction to computational fluid dynamics, the finite volume method, Longman Group, U.K.
Warrick, A. W. (1974). “Time dependent linearized infiltration: I. Point sources.” Soil Sci. Soc. Am. Proc., 38(3), 383–386.
Warrick, A. W., and Lomen, D. O. (1976). “Time-dependent linearized infiltration: III. Strip and disc sources.” Soil Sci. Soc. Am. J., 40(5), 639–643.
Wooding, R. A. (1968). “Steady infiltration from a shallow circular pond.” Water Resour. Res., 4(6), 1259–1273.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 141 • Issue 4 • April 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Nov 10, 2013
Accepted: Aug 12, 2014
Published online: Sep 15, 2014
Discussion open until: Feb 15, 2015
Published in print: Apr 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.