- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 491317, 15 pages
A Numerical Treatment of Nondimensional Form of Water Quality Model in a Nonuniform Flow Stream Using Saulyev Scheme
1Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand
2Centre of Excellence in Mathematics, Commission on Higher Education (CHE), Si Ayutthaya Road, Bangkok 10400, Thailand
Received 11 April 2011; Revised 21 June 2011; Accepted 6 July 2011
Academic Editor: Delfim Soares Jr.
Copyright © 2011 Nopparat Pochai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. Garzon and L. D’Alpaos, “A modified method of the characteristic technique combined with Gelerkin finite element method to solve shallow water mass transport problems,” in Proceedings 23rd International Conference in Coastal Engineering, vol. 3, pp. 3068–3080, 1992.
- N. Pochai, S. Tangmanee, L. J. Crane, and J. J. H. Miller, “A mathematical model of water pollution control using the finite element method,” Proceedings in Applied Mathematics and Mechanics, vol. 6, no. 1, pp. 755–756, 2006.
- J. Y. Chen, C. H. Ko, S. Bhattacharjee, and M. Elimelech, “Role of spatial distribution of porous medium surface charge heterogeneity in colloid transport,” Colloids and Surfaces A, vol. 191, no. 1-2, pp. 3–15, 2001.
- G. Li and C. R. Jackson, “Simple, accurate, and efficient revisions to MacCormack and Saulyev schemes: high Peclet numbers,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 610–622, 2007.
- E. M. O'Loughlin and K. H. Bowmer, “Dilution and decay of aquatic herbicides in flowing channels,” Journal of Hydrology, vol. 26, no. 3-4, pp. 217–235, 1975.
- M. Dehghan, “Numerical schemes for one-dimensional parabolic equations with nonstandard initial condition,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 321–331, 2004.
- A. I. Stamou, “Improving the numerical modeling of river water quality by using high order difference schemes,” Water Research, vol. 26, no. 12, pp. 1563–1570, 1992.
- S. Marušić, “Natural convection in shallow water,” Nonlinear Analysis: Real World Applications, vol. 8, no. 5, pp. 1379–1389, 2007.
- A. Dube and G. Jayaraman, “Mathematical modelling of the seasonal variability of plankton in a shallow lagoon,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 3, pp. 850–865, 2008.
- D. Ionescu-Kruse, “Particle trajectories beneath small amplitude shallow water waves in constant vorticity flows,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 9, pp. 3779–3793, 2009.
- P. Tabuenca, J. Vila, and J. Cardona, “Finite element simulation of dispersion in the Bay of Santander,” Advances in Engineering Software, vol. 28, no. 5, pp. 313–332, 1997.
- N. Pochai, “A numerical computation of the non-dimensional form of a non-linear hydrodynamic model in a uniform reservoir,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 4, pp. 463–466, 2009.
- N. Pochai, S. Tangmanee, L. J. Crane, and J. J. H. Miller, “A water quality computation in the uniform channel,” Journal of Interdisciplinary Mathematics, vol. 11, no. 6, pp. 803–814, 2008.
- N. Pochai, “A numerical computation of a non-dimensional form of stream water quality model with hydrodynamic advection-dispersion-reaction equations,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 4, pp. 666–673, 2009.
- S. C. Chapra, Surface Water-Quality Modeling, McGraw-Hill, New York, NY, USA, 1997.
- H. Ninomiya and K. Onishi, Flow Analysis Using a PC, CRC Press, Boca Raton, Fla, USA, 1991.
- A. R. Mitchell, Computational Methods in Partial Differential Equations, John Wiley & Sons, London, UK, 1969.
- W. F. Ames, Numerical Methods for Partial Differential Equations, Computer Science and Scientific Computing, Academic Press, Boston, Mass, USA, 2nd edition, 1977.
- M. Dehghan, “Weighted finite difference techniques for the one-dimensional advection-diffusion equation,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 307–319, 2004.
- W. Zeng, A model for understanding and managing the impacts of sediment behavior on river water quality, Ph.D. thesis, University of Georgia, Athens, Ga, USA, 2000.
- L. Lapidus and G. F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering, John Wiley & Sons, New York, NY, USA, 1982.