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Abstract and Applied Analysis
Volume 2018, Article ID 1926519, 7 pages
https://doi.org/10.1155/2018/1926519
Research Article

Numerical Simulation of a One-Dimensional Water-Quality Model in a Stream Using a Saulyev Technique with Quadratic Interpolated Initial-Boundary Conditions

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

Correspondence should be addressed to Nopparat Pochai; moc.oohay@htam_pon

Received 13 October 2017; Revised 10 December 2017; Accepted 26 December 2017; Published 1 February 2018

Academic Editor: Tongxing Li

Copyright © 2018 Pawarisa Samalerk and 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.

Linked References

  1. 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. View at Publisher · View at Google Scholar
  2. D. B. Spalding, “A novel finite difference formulation for differential expressions involving both first and second derivatives,” International Journal for Numerical Methods in Engineering, vol. 4, no. 4, pp. 551–559, 1972. View at Publisher · View at Google Scholar · View at Scopus
  3. J. P. Boris and D. L. Book, “Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works,” Journal of Computational Physics, vol. 11, no. 1, pp. 38–69, 1973. View at Publisher · View at Google Scholar · View at Scopus
  4. R. J. Sobey, “Fractional step algorithm for estuarine mass transport,” International Journal for Numerical Methods in Fluids, vol. 3, no. 6, pp. 567–581, 1983. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. S. Li and J. P. Ward, “An efficient split-operator scheme for 2-D advection-diffusion equation using finite elements and characteristics,” Applied Mathematical Modelling, vol. 13, no. 4, pp. 248–253, 1989. View at Publisher · View at Google Scholar · View at Scopus
  6. B. J. Noye and H. H. Tan, “A third-order semi-implicit finite difference method for solving the one-dimensional convection diffusion equation,” Applied Mathematical Modeling, vol. 13, pp. 248–253, 1988. View at Google Scholar
  7. D. C. L. Lam, “Computer modeling of pollutant transport in Lake Erie,” Water Pollution, vol. 25, pp. 75–89, 1975. View at Google Scholar
  8. B. P. Leonard, “A stable and accurate convective modelling procedure based on quadratic upstream interpolation,” Computer Methods Applied Mechanics and Engineering, vol. 19, no. 1, pp. 59–98, 1979. View at Publisher · View at Google Scholar · View at Scopus
  9. 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. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. H. Karahan, “Unconditional stable explicit finite difference technique for the advection-diffusion equation using spreadsheets,” Advances in Engineering Software, vol. 38, no. 2, pp. 80–86, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. N. Pochai, “A numerical treatment of nondimensional form of water quality model in a nonuniform flow stream using Saulyev scheme,” Mathematical Problems in Engineering, vol. 2011, Article ID 491317, 15 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. N. Pochai, “Numerical treatment of a modified MacCormack scheme in a nondimensional form of the water quality models in a nonuniform flow stream,” Journal of Applied Mathematics, vol. 2014, Article ID 274263, 8 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  13. 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. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. B. M. Chen-Charpentier and H. V. Kojouharov, “An unconditionally positivity preserving scheme for advection-diffusion reaction equations,” Mathematical and Computer Modelling, vol. 57, no. 9-10, pp. 2177–2185, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Y. Yi, C. Tang, Z. Yang, S. Zhang, and C. Zhang, “A one-dimensional hydrodynamic and water quality model for a water transfer project with multihydraulic structures,” Mathematical Problems in Engineering, vol. 2017, pp. 1–11, 2017. View at Publisher · View at Google Scholar
  16. K. Thongtha and J. Kasemsuwan, “Analytical solution to a hydrodynamic model in an open uniform reservoir,” Advances in Difference Equations, vol. 2017, p. 149, 2017. View at Google Scholar · View at MathSciNet
  17. N. Pochai, “Unconditional stable numerical techniques for a water-quality model in a non-uniform flow stream,” Advances in Difference Equations, vol. 2017, p. 286, 2017. View at Google Scholar · View at MathSciNet
  18. C. Zhu, Q. Liang, F. Yan, and W. Hao, “Reduction of waste water in erhai lake based on MIKE21 hydrodynamic and water quality model,” The Scientific World Journal, vol. 2013, Article ID 958506, 9 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. R. L. Burden and J. D. Faires, Numerical Analysis, Brook and Cole, Boston, Mass, USA, 9th edition, 2011. View at Publisher · View at Google Scholar