Numerical optimization for the purification of polluted shallow waters

The optimal control theory allows us to design a wastewater treatment system in order to control marine pollution in any open area of shallow waters, as was shown in previous works of the authors. However, there exist many closed areas (for instance, enclosed bays) which present a serious quality problem caused by domestic/industrial contaminants, due to the insufficient seawater exchange. In these areas it is necessary to consider a new technique in order to purify polluted waters: promoting seawater exchange by the injection of clear water from the outer sea. The aim of this paper is to determine the minimal quantity of injected water in order to purify the protected areas up to a fixed threshold. We present the mathematical formulation of the continuous and discretized control problems, and propose an algorithm for the numerical resolution. Finally, we present numerical results obtained in the study of a real-world problem.