Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer

Azhari Ahmad Abdalla

doi:doi:10.11648/j.pamj.20160501.13

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Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer

Azhari Ahmad Abdalla

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 1)

Received: 1 January 2016 Accepted: 21 January 2016 Published: 1 February 2016

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Abstract

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.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 1)
DOI	10.11648/j.pamj.20160501.13
Page(s)	15-22
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

BIEM, Unconfined Aquifer, Dupuit Assumption, Groundwater Flow

References

[1]	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.
[2]	Albrecht, J. and Collaty, L. (Eds.), (1980) "Numerical Treatment of Integral Equations", Birkhauser Verlag, Basel, 1980.
[3]	Bear. Jacob, (1978). Dynamic of Fluid in Porous Media, Dover Books on Engineering, ISBN-13: 978-0486453552
[4]	Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., (1984), Boundary Elements Techniques. Springer-Verlag, Berlin, 1984.
[5]	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.
[6]	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.
[7]	Goldberg, M. A. (Ed.), (1979), "Solution Methods for Integral Equations: Theory and Applications, Plenum Press, New York, 1979.
[8]	James A, Ligett, Philip L-F. Liu, (1983) "The Boundary Integral Equation Method for Porous Media Flow", London, George Allen and UNWIN, 1983.
[9]	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.
[10]	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.
[11]	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.
[12]	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.
[13]	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.
[14]	Norrie, D. H. and de Vries, G. (1978) "An Introduction to Finite Element Analysis ll, Academic Press, New York, 1978.
[15]	Phoolendra K. Mishra and Kristopher L. Kuhlman (2013), Unconfined Aquifer Flow Theory - from Dupuit to present, physics. flu. dyn
[16]	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.

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Azhari Ahmad Abdalla. (2016). Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer. Pure and Applied Mathematics Journal, 5(1), 15-22. https://doi.org/10.11648/j.pamj.20160501.13

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ACS Style

Azhari Ahmad Abdalla. Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer. Pure Appl. Math. J. 2016, 5(1), 15-22. doi: 10.11648/j.pamj.20160501.13

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AMA Style

Azhari Ahmad Abdalla. Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer. Pure Appl Math J. 2016;5(1):15-22. doi: 10.11648/j.pamj.20160501.13

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@article{10.11648/j.pamj.20160501.13,
  author = {Azhari Ahmad Abdalla},
  title = {Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {1},
  pages = {15-22},
  doi = {10.11648/j.pamj.20160501.13},
  url = {https://doi.org/10.11648/j.pamj.20160501.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160501.13},
  abstract = {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.},
 year = {2016}
}

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TY  - JOUR
T1  - Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer
AU  - Azhari Ahmad Abdalla
Y1  - 2016/02/01
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160501.13
DO  - 10.11648/j.pamj.20160501.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 15
EP  - 22
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160501.13
AB  - 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.
VL  - 5
IS  - 1
ER  -

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Author Information

Azhari Ahmad Abdalla

Department of Mathematics, Prep-Year, University of Hail, Hail, Saudi Arabia

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APA Style

Azhari Ahmad Abdalla. (2016). Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer. Pure and Applied Mathematics Journal, 5(1), 15-22. https://doi.org/10.11648/j.pamj.20160501.13

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ACS Style

Azhari Ahmad Abdalla. Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer. Pure Appl. Math. J. 2016, 5(1), 15-22. doi: 10.11648/j.pamj.20160501.13

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AMA Style

Azhari Ahmad Abdalla. Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer. Pure Appl Math J. 2016;5(1):15-22. doi: 10.11648/j.pamj.20160501.13

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@article{10.11648/j.pamj.20160501.13,
  author = {Azhari Ahmad Abdalla},
  title = {Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {1},
  pages = {15-22},
  doi = {10.11648/j.pamj.20160501.13},
  url = {https://doi.org/10.11648/j.pamj.20160501.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160501.13},
  abstract = {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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer
AU  - Azhari Ahmad Abdalla
Y1  - 2016/02/01
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160501.13
DO  - 10.11648/j.pamj.20160501.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 15
EP  - 22
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160501.13
AB  - 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.
VL  - 5
IS  - 1
ER  -

Copy | Download