Advertisement

Optimizing Water Quality in a River Section

  • M. A. Vilar
  • L. J. Alvarez-Vázquez
  • A. Martínez
  • M. E. Vázquez-Méndez

Abstract

Since early times, rivers have been not only sources of life but also water discharge receivers (both from industrial and urban origin) from the human settlements on their banks. This fact brings with it that pollutant matter concentration surpasses healthy levels in some sections of the rivers. In our paper, we use mathematical modeling and optimal control theory to simulate one of most common strategies in the pollution reduction of a river section: clear water injection into the channel from a nearby reservoir. In this process of increasing the river flow by controlled releases of water from reservoirs, the main problem consists (once the injection point has been chosen by geophysical reasons) of finding the minimum quantity of water which needs to be injected into the river section in order to purify it to a desired level.

Keywords

Admissible Control Optimal Control Theory River Section Water Quality Analysis Exact Penalty Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Al02]
    Alvarez-Vázquez, L.J., Martínez, A., Rodríguez, C., Vázquez-Méndez, M.E.: Numerical optimization for the location of wastewater outfalls. Comput. Optim. Appl., 22, 399–417 (2002). MathSciNetMATHCrossRefGoogle Scholar
  2. [Al06]
    Alvarez-Vázquez, L.J., Martínez, A., Vázquez-Méndez, M.E., Vilar, M.A.: Optimal location of sampling points for river pollution control. Math. Comput. Simul., 71, 149–160 (2006). MATHCrossRefGoogle Scholar
  3. [Al09]
    Alvarez-Vázquez, L.J., Martínez, A., Vázquez-Méndez, M.E., Vilar, M.A.: An application of optimal control theory to river pollution remediation. Appl. Numer. Math., 59, 845–858 (2009). MathSciNetMATHCrossRefGoogle Scholar
  4. [Be81]
    Bermúdez, A., Moreno, C.: Duality methods for solving variational inequalities. Comput. Math. Appl., 7, 43–58 (1981). MathSciNetMATHCrossRefGoogle Scholar
  5. [Be06]
    Bermúdez, A., Muñoz-Sola, R., Rodríguez, C., Vilar, M.A.: Theoretical and numerical study of an implicit discretization of a 1D inviscid model for river flows. Math. Models Meth. Appl. Sci., 16, 375–395 (2006). MATHCrossRefGoogle Scholar
  6. [Br73]
    Brezis, H.: Operateurs Maximaux Monotones el Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam (1973). Google Scholar
  7. [Ne65]
    Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer J., 7, 308–313 (1965). MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • M. A. Vilar
    • 1
  • L. J. Alvarez-Vázquez
    • 2
  • A. Martínez
    • 2
  • M. E. Vázquez-Méndez
    • 1
  1. 1.Universidad de SantiagoLugoSpain
  2. 2.Universidad de VigoVigoSpain

Personalised recommendations