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A DUAL-RECIPROCITY BOUNDARY ELEMENT METHOD FOR STEADY INFILTRATION PROBLEMS

Part of: Basic methods in fluid mechanics

Published online by Cambridge University Press:  18 July 2013

I. SOLEKHUDIN  and
K. C. ANG
I. SOLEKHUDIN*
Affiliation:
Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore email kengcheng.ang@nie.edu.sg Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Yogyakarta 55281, Indonesia email imam.solekhudin@stdmail.nie.edu.sg
K. C. ANG
Affiliation:
Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore email kengcheng.ang@nie.edu.sg
*
✉imams@ugm.ac.id
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Abstract

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Steady water infiltration in homogeneous soils is governed by the Richards equation. This equation can be studied more conveniently by transforming to a type of Helmholtz equation. In this study, a dual-reciprocity boundary element method (DRBEM) is employed to solve the Helmholtz equation numerically. Using the solutions obtained, numerical values of the suction potential are then computed. The proposed method is tested on problems involving infiltration from different types of periodic channels in a homogeneous soil. Moreover, the method is also examined using infiltration from periodic trapezoidal channels in three different types of homogeneous soil.

Keywords

Richards equationsuction potentialdual-reciprocity boundary element methodperiodic identical irrigation channels

MSC classification

Secondary: 76M15: Boundary element methods

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 54 , Issue 3 , January 2013 , pp. 171 - 180
Copyright
Copyright ©2013 Australian Mathematical Society 

References

Amoozegar-Fard, A., Warrick, A. W. and Lomen, D. O., “Design nomographs for trickle irrigation systems”, J. Irrigation Drainage Engrg. 110 (1984) 107–120; doi:10.1061/(ASCE)0733-9437(1984)110:2(107).CrossRefGoogle Scholar
Ang, W. T., “A Laplace transformation dual-reciprocity boundary element method for a class of two-dimensional microscale thermal problems”, Engrg. Comput. 19 (2002) 467–478; doi:10.1108/02644400210430217.CrossRefGoogle Scholar
Ang, W. T. and Ang, K. C., “A dual-reciprocity boundary element solution of a generalized nonlinear Schrödinger equation”, Numer. Methods Partial Differential Equations 20 (2004) 843–854; doi:10.1002/num.20011.CrossRefGoogle Scholar
Azis, M. I., Clements, D. L. and Lobo, M., “A boundary element method for steady infiltration from periodic channels”, ANZIAM J. 44 (2003) C61–C78; http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/672.CrossRefGoogle Scholar
Batu, V., “Steady infiltration from single and periodic strip sources”, Soil Sci. Soc. Am. J. 42 (1978) 544–549; doi:10.2136/sssaj1978.03615995004200040033x.CrossRefGoogle Scholar
Brebbia, C. A. and Nardini, D., “Dynamic analysis in solid mechanics by an alternative boundary element procedure”, Int. J. Soil Dynam. Earthquake Engrg. 2 (1983) 228–233; doi:10.1016/0261-7277(83)90040-2.CrossRefGoogle Scholar
Bresler, E., “Analysis of trickle irrigation with application to design problems”, Irrigation Sci. 1 (1978) 3–17; doi:10.1007/BF00269003.CrossRefGoogle Scholar
Clements, D. L., Lobo, M. and Widana, N., “A hypersingular boundary integral equation for a class of problems concerning infiltration from periodic channels”, Electron. J. Bound. Elem. 5 (2007) 1–16; http://ejbe.libraries.rutgers.edu/index.php/ejbe/article/view/779.Google Scholar
Lobo, M., Clements, D. L. and Widana, N., “Infiltration from irrigation channels in a soil with impermeable inclusions”, ANZIAM J. 46 (2005) C1055–C1068; http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1006.CrossRefGoogle Scholar
Philip, J. R., “Flow in porous media”, Annu. Rev. Fluid Mech. 2 (1970) 177–204; doi:10.1146/annurev.fl.02.010170.001141.CrossRefGoogle Scholar
Pullan, A. J., “Linearized time-dependent infiltration from a shallow pond”, Water Resour. Res. 28 (1992) 1041–1046; doi:10.1029/91WR03032.CrossRefGoogle Scholar
Waechter, R. T. and Mandal, A. C., “Steady infiltration from a semicircular cylindrical trench and a hemispherical pond into unsaturated soil”, Water Resour. Res. 29 (1993) 457–467; doi:10.1029/92WR02089.CrossRefGoogle Scholar
Waechter, R. T. and Philip, J. R., “Steady two- and three-dimensional flows in unsaturated soil: the scattering analog”, Water Resour. Res. 21 (1985) 1875–1887; doi:10.1029/WR021i012p01875.CrossRefGoogle Scholar
Zhu, S. P., Satravaha, P. and Lu, X. P., “Solving linear diffusion equations with the dual reciprocity method in Laplace space”, Eng. Anal. Bound. Elem. 13 (1994) 1–10; doi:10.1016/0955-7997(94)90002-7.CrossRefGoogle Scholar