A New Two Dimensional Model for Pollutant Transport in Ajichai River

Document Type : Research Paper


Faculty of Water Engineering, University of Zabol, Zabol, Iran


Accurate prediction of pollution control and environmental protection need a good understanding of pollutant dynamics. Numerical model techniques are important apparatus in this research area. So a 2500 line FORTRAN 95 version code was conducted in which using approximate Riemann solver, couples the shallow water and pollution transport agents in two dimensions by the aid of unstructured meshes. A multidimensional linear reconstruction technique and multidimensional slope limiter were implemented to achieve a second-order spatial accuracy. The courant number ruled as a control parameter for stability conditions and a third order Runge-Kutta method was performed for equation discretizations. For Code verifications another author's case study was examined.
The numerical results show that the model could accurately predict the flow dynamics and pollutant transport in Ajichai River.


  1. Alcrudo F., F. Benkhaldoun, ”Exact Solutions to the Riemann Problem of the Shallow Water Equations with a Bottom Step”, Comput. Fluids. 30, 643–671 (2001).
  2. Benkhaldoun, F. ”Analysis and Validation of a new Finite Volume Scheme for Nonhomoge- neous Systems”, Finite Volumes for Complex Applications IV: Problems & Perspectives, Hermes Science Publications, R. Herbin, D. Kroner Eds. 269–276 (2002).
  3. Benkhaldoun F., L. Quivy, ”A Non Homogeous Riemann Solver for Shallow Water and Two Phase Flows”, Flow Turbulence Combustion. 76 391–402 (2006).
  4. Benkhaldoun F. , Elmahi I. , Seaid M. , 2007, Well-balanced finite volume schemes for pollutant transport on unstructured meshes, pp 180-203. Journal of Computational Physics 226, 1 (2007) 180–203.
  5. Delis AI. Improved application of the HLLE Riemann solver for the shallow water equations with source terms. Commun. Numer. Meth. Eng. 2003; 19:59-83.
  6. Heniche M., Y. Secretan, P. Boudreau, M. Leclerc, ”A Two-Dimensional Finite Element Drying-Wetting Shallow Water Model for Rivers and Estuaries”, Advances in Water Resources.23, 359–372 (2000).
  7. James I.D. , ”Modelling Pollution Dispersion, the Ecosystem and Water Quality in Coastal Waters: A Review”, Environ. Model Software. 17, 363–385 (2002).
  8. Jawahar P, Kamath H. A high-resolution procedure for Euler and Navier-Stokes computations on unstructured grids. Journal of Computational Physics 2000; 164: 165-203.
  9. Komatsu T, Ohgushi K, Asai K. Refined numerical scheme for advective transport in diffusion simulation. J. Hydraulic Eng. 1997; 123: 41–50.
  10. Komatsu T., K. Ohgushi, K. Asai, ”Refined numerical scheme for advective transport in diffusion simulation”, J. Hydraulic Eng. 123, 41–50 (1997).
  11. Lin B., R.A. Falconer, ”Tidal flow and transport modeling using ultimate quickest scheme”, J. Hydraulic Eng. 123, 303–314 (1997).
  12. Roe P.L. , ”Approximate Riemann Solvers, Parameter Vectors and Difference Schemes”, J. Comp. Physics. 43, 357-372 (1981).
  13. Toro E.F. , ”Shock-Capturing Methods for Free-Surface Shallow Waters”, Wiley Chichester2001.
  14. V´azquez M.E., ”Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry”, J. Comp. Physics. 148, 497–526 (1999).
  15. Zhou JG, Causon DM, Mingham CG, Ingram DM.The Surface Gradient Method for the Treatment of Source Terms in the Shallow-Water Equations. J Comput Phys 2001; 168: 1-25.