Abstract
This work analyzes, from a mathematical point of view, the artificial mixing of water -by means of several pairs collector/injector that set up a circulation pattern in the waterbody -in order to prevent the undesired effects of eutrophication. The environmental problem is formulated as a constrained optimal control problem of partial differential equations, where the state system is related to the velocity of water and to the concentrations of the different species involved in the eutrophication processes, and the cost function to be minimized represents the volume of recirculated water. In the main part of the work, the wellposedness of the problem and the existence of an optimal control is demonstrated. Finally, a complete numerical algorithm for its computation is presented, and some numerical results for a realistic problem are also given.
Highlights
Artificial circulation and aeration are management techniques for oxygenating eutrophic waterbodies subject to quality problems, such as loss of oxygen, sediment accumulation and algal blooms
Artificial circulation disrupts stratification and minimizes the development of stagnant zones that may be subject to water quality problems
The movement of water and/or air is accomplished by use of bottom diffusers and water pumps to create a circulation pattern in shallow waters [11]
Summary
Artificial circulation and aeration are management techniques for oxygenating eutrophic waterbodies subject to quality problems, such as loss of oxygen, sediment accumulation and algal blooms. A flow pump takes water from the epilimnion (well aerated upper layer of water) by means of a collector, injecting it into the hypolimnion (poorly oxygenated bottom layer), setting up a circulation pattern that prevents stratification. In this way, oxygen-poor water from the bottom is circulated to the surface, where oxygenation from the atmosphere can occur. We present first the hydrodynamic model, and the model for the evolution of the concentrations of the different species involved in the eutrophication processes
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