Keywords: pollutant dispersion, convection-diffusion equation, finite element methods, explicit characteristic-based method, thermal outflow, Huelva estuary.

A simple explicit, characteristic-based finite element method [1] for the numerical simulation of the dispersion of thermal outlow in the Huelva estuary is studied in this presentation. The derivation involves a local Taylor expansion of the convection-diffusion equation. The numerical model used, called SEASCAPE [2,3] which stands for Simple Explicit GAlerkin Procedure to Solve Convection-Diffusion EquAtion in the OPen SEa, was originally designed to simulate the dispersion of the of pollutants in the open sea [4] and has now been reconfigured to simulate the dispersion of thermal outflow of some power plants which may be constructed in the Huelva Estuary in the near future. Numerical results obtained are presented.

In term of accuracy, stability and convergence properties, the simple explicit Characteristic-Galerkin method was chosen to solve the convection-diffusion equation. This method has the required properties which include the introduction of the stabilizing term or artificial viscosity that stabilises the convective oscillations.

The method starts from a particular time discretization of the differential equation before obtaining the weak form. Time discretization is based on Taylor expansion of the convection-diffusion equation.

The dispersion of contaminants in bodies of water is intrinsically three- dimensional but due to high computational cost of three-dimensional discretization, we opted to use a quasi-3D approximation. The basic idea of the quasi-3D model is the combination of the conventional 2DH model and a local 1DV model that describes the vertical distribution of the concentration of the contaminants through its decomposition in base function and profile. The standard Galerkin method of weighted residuals is applied on the time discretized equations where vertical variation of the unknown variables is approximated by a linear combination of known basis function attached to each nodal value or degree of freedom.

The magnitude of the variable is discretized horizontally to eliminate the x and y dependence. The horizontal variations of the variables of the problem are interpolated using the isoparametric finite element basis function sufficient to interpolate the diffusive terms. Galerkin method of weighted residuals is applied and integration by parts is employed to reduce the second order partial derivatives to first order.

The algorithm is implemented in the numerical model named SEASCAPE to simulate the dispersion of thermal outflow of some power plants that might be constructed in the Huelva estuary. The computational grid used has 3200 quadrilateral elements and 3531 nodes. Data for the mean flow and numerical propagation of tides required to simulate the dynamics of the estuary were culled from previously formulated numerical models such as NAUTILUS [5,6] and MAREAS [7]. The value of the coefficient of diffusivity K_H was set at 10m²/s [8]. A homogenous Neumann boundary condition is prescribed on the mouth of Tinto river and Dirichlet boundary conditions are imposed on the locations of the wastewater discharges. Simulation results, when all three power plants are discharging water into the estuary, show that substantial increase in water temperature can be observed at the end of the simulation period. Contaminant dispersion does not reach a stationary condition even after the simulation period has elapsed. The simulation period must be prolonged to see how the thermal outflow will evolve.

The numerical results presented show that the numerical model provides a comprehensive and efficient tool to simulate contaminant dispersion.

1

Zienkiewics, O.C. and Taylor, R.L. "El Metodo de los Elementos Finitos", Madrid:McGraw-Hill/Interamerica de España, S.A 6(4), 20-24, 1995

2

Hermosilla, F. "Estudio de la Dispersión de Contaminantes en el Mar Mediante el MEF", Master Thesis, UPC, Barcelona, 1996

3

German, A. "An Explicit, Characteristics-Based Finite Element Method for the Numerical Simulation of the Dispersion of Pollutants in the Sea", Master Thesis, CIMNE-UPC, Barcelona, 1999

4

Lewis, R. "Dispersion in Estuaries and Coastal Waters", Chichester: John Wiley and Son Ltd, 1997

5

Espino, M., Sánchez-Arcilla, A. and García, M.A., "Wind-induced mesoscale circulation off the Ebro delta, NW Mediterranean: A Numerical Study", Journal of Marine Systems, 16. 235-251, 1998. doi:10.1016/S0924-7963(97)00110-3

6

Maidana M.A., Naudin J.J., Espino M., García M.A. and Sánchez-Arcilla A., "Feasibility and usefulness of diagnostic calculations of the mean circulation in the vicinity of the Ebro mouth. Model tests against field data", Continental Shelf Research, 22. 229-245, 2002. doi:10.1016/S0278-4343(01)00055-3

7

Gonzáles, M., García, M.A., Espino, M. and Sánchez-Arcilla A., "Un modelo numérico en elementos finitos para la corriente inducida por la marea. Aplicaciones al estrecho de Gibraltar", Revista Internacional de Métodos Numéricos para el Cálculo y Diseño en Ingeniería, Vol.11, 3. 383.

8

Maidana, M.A., Espino, M., Comerma, E., Sánchez-Arcilla, A., Ayora, C. and Palanques, A., "A hydrodynamic study of the Huelva estuary. Tidal model calibration using field data", RCEM 2003 Vol. II, 697-709

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £95 +P&P)