Mathematical modelling and optimal control
methods in water pollution
Alfredo Bermudez
Department of Applied Mathematics
University of Santiago de Compostela
Campus Universitario
15706 Santiago de Compostela. SPAIN.
Introduction
In the last years increasing attention has been paid to reduce the environmental impact
of domestic and industrial wastewater discharges. As the objective of non-polluting effiuent disposal alternatives is limited by technical or financial factors, an outfall is sometimes
the only feasible solution (see Quetin & De Rouville [1986]).
The main objective of a sea outfall is to discharge effiuent from a sewerage system
at an adequate distance from populated coastal areas. Implementation requires studies
to predict pollutant concentrations at points of the discharge area, assuming various
possible discharge points. Then a selection is made according to general advantages
as economy, proximity to a planned sewage plant, etc. However some constraints exist
because of regulations on permitted maximum pollution concentration in areas of bath,
marine cultures, etc.
In these studies, mathematical models are extensively used to predict pollutant concentration (see for instance Brebbia [1976], Nihoul [1975], Ames [1988], Gambolati, Rinaldo,
Brebbia, Gray & Pinder [1990], Bermudez [1993], [1994]). Two main types of models exist
corresponding to the two following stages of effiuent flow:
• Buoyant flow from the point of discharge towards the surface (nearfield)
• Horizontal transport by current action from the final level in the previous stage
(farfield)
Currents are very often the main factor for dispersion of pollutants in farfteld. Hence,
in a first step, we are concerned with mathematical models for hydrodynamics in coastal
areas, lakes, rivers, etc. More precisely we will recall the shallow water equations and
those modelling flow in rivers.
NATO ASI Series. Vol. I 48
The Mathematics of Models for Climatology
and Environment
Edited by Jesus IIdefonso Diaz
© Springer-Verlag Berlin Heidelberg 1997
methods in water pollution
Alfredo Bermudez
Department of Applied Mathematics
University of Santiago de Compostela
Campus Universitario
15706 Santiago de Compostela. SPAIN.
Introduction
In the last years increasing attention has been paid to reduce the environmental impact
of domestic and industrial wastewater discharges. As the objective of non-polluting effiuent disposal alternatives is limited by technical or financial factors, an outfall is sometimes
the only feasible solution (see Quetin & De Rouville [1986]).
The main objective of a sea outfall is to discharge effiuent from a sewerage system
at an adequate distance from populated coastal areas. Implementation requires studies
to predict pollutant concentrations at points of the discharge area, assuming various
possible discharge points. Then a selection is made according to general advantages
as economy, proximity to a planned sewage plant, etc. However some constraints exist
because of regulations on permitted maximum pollution concentration in areas of bath,
marine cultures, etc.
In these studies, mathematical models are extensively used to predict pollutant concentration (see for instance Brebbia [1976], Nihoul [1975], Ames [1988], Gambolati, Rinaldo,
Brebbia, Gray & Pinder [1990], Bermudez [1993], [1994]). Two main types of models exist
corresponding to the two following stages of effiuent flow:
• Buoyant flow from the point of discharge towards the surface (nearfield)
• Horizontal transport by current action from the final level in the previous stage
(farfield)
Currents are very often the main factor for dispersion of pollutants in farfteld. Hence,
in a first step, we are concerned with mathematical models for hydrodynamics in coastal
areas, lakes, rivers, etc. More precisely we will recall the shallow water equations and
those modelling flow in rivers.
NATO ASI Series. Vol. I 48
The Mathematics of Models for Climatology
and Environment
Edited by Jesus IIdefonso Diaz
© Springer-Verlag Berlin Heidelberg 1997