Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer
Pure and Applied Mathematics Journal
Volume 5, Issue 1, February 2016, Pages: 15-22
Received: Jan. 1, 2016;
Accepted: Jan. 21, 2016;
Published: Feb. 1, 2016
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Azhari Ahmad Abdalla, Department of Mathematics, Prep-Year, University of Hail, Hail, Saudi Arabia
In this paper, we employed the use of Boundary Integral Equation Method to obtain numerical solutions of specific unconfined aquifer flow problems. Of the two formulations presented in this paper, that in which the piezometric head and its normal derivative are assumed to vary linearly with time over each time step has proved more accurate than that in which both piezometric head and its normal derivative remain constant at each node throughout each time step. Comparisons between Method 2 of section-3 and the analytical solutions have demonstrated the superior accuracy of the integral equation formulation.
Azhari Ahmad Abdalla,
Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer, Pure and Applied Mathematics Journal.
Vol. 5, No. 1,
2016, pp. 15-22.
ALI A Ameli (2014), "Semi-analytical methods for simulating the groundwater-surface water interface", in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Civil Engineering Waterloo, Ontario, Canada.
Albrecht, J. and Collaty, L. (Eds.), (1980) "Numerical Treatment of Integral Equations", Birkhauser Verlag, Basel, 1980.
Bear. Jacob, (1978). Dynamic of Fluid in Porous Media, Dover Books on Engineering, ISBN-13: 978-0486453552
Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., (1984), Boundary Elements Techniques. Springer-Verlag, Berlin, 1984.
Dupuit, J. (1863). Estudes Théoriques et Pratiques sur le mouvement des Eaux dans les canaux découverts et à travers les terrains perméables (Second ed.). Paris: Dunod.
Dubois, M. and Buysse, M., (1980), "Transient Heat Transfer Analysis by the Boundary Integral Equation Method", in New Developments in Boundary Element Methods, Brebbia, Co (Ed.), C. M. L. Publications, Southampton, 1980.
Goldberg, M. A. (Ed.), (1979), "Solution Methods for Integral Equations: Theory and Applications, Plenum Press, New York, 1979.
James A, Ligett, Philip L-F. Liu, (1983) "The Boundary Integral Equation Method for Porous Media Flow", London, George Allen and UNWIN, 1983.
Lafe, O. E., Liggett, J. A. and Liu, P. L. F. (1981) "BIEM Solutions to Combinations of Leaky, Layered, Confined, Unconfined, Nonisotropic Aquifers ll, Water Resources Research, Vol. lJ, No. 5, pp. 1431-1444, October, 1981.
Lennon, G. P., Liu, P. L. F. and Liggett, J. A. (1979) "Boundary Integral Equation Solution to Axisymmetric Potential Flows; 1. Basic Formulation; 2. Recharge and Well Problems in Porous Media ll Water Resources Research, Vol. 15, No. 5, pp. 1102-1115, October, 1979.
Lennon, G. P., Liu, 1 L. F. and Liggett, J. A. (1980) "Boundary Integral Solutions to Three-Dimensional Unconfined Darcy's Flow", Water Resources Research, Vol. 16, No. 4, pp. 65 658, August, 1980.
Massonnet, C. E. (1965) "Numerical Use of Integral Procedures in Stress Analysis", Zienkiewicz, O. C. and Holister, G. S. (Eds.), John Wiley and Sons, Inc., New York.
M. N. Vu a, n, S. T. Nguyen a, c, M. H. Vu a, b, (2015)," Modeling of fluid flow through fractured porous media by a single boundary integral equation", Engineering Analysis with Boundary Elements 59 (2015) 166–171.
Norrie, D. H. and de Vries, G. (1978) "An Introduction to Finite Element Analysis ll, Academic Press, New York, 1978.
Phoolendra K. Mishra and Kristopher L. Kuhlman (2013), Unconfined Aquifer Flow Theory - from Dupuit to present, physics. flu. dyn
Wrobel, L. C. and Brebbia, C. A. (1981), "A Formulation of the Boundary Element Method for Axisymmetric Transient Heat Conduction", International Journal of Heat and Mass Transfer, Vol. 24, No. 5, pp. 843-850, 1981.