Miguel A. Vilar

Optimal location of sampling points for river pollution control

Common methods of controlling river pollution include establishing water pollution monitoring stations located along the length of the river. The point where each station is located (sampling point) is of crucial importance and, obviously, depends on the reasons for the sample. Collecting data about pollution at selected points along the river is not the only objective; must also be extrapolated to know the characteristics of the pollution in the entire river. In this work we will deal with the optimal location of sampling points. A mathematical formulation for this problem as well as an efficient algorithm to solve it will be given. Finally, in last sections, we will present numerical results obtained by using this algorithm when applied to a realistic situation in a river mouth.

Optimal shape design for fishways in rivers

Fishways are hydraulic structures that enable fish to overcome obstructions to their spawning and other migrations in rivers. In this paper we first introduce a mathematical formulation of the optimal design problem for a vertical slot fishway, where the state system is given by the shallow water equations determining the height of water and its velocity, the design variables are the geometry of the slots, and the objective function is related to the existence of rest areas for fish and a water velocity suitable for fish leaping and swimming capabilities. We also obtain an expression for the gradient of the objective function via the adjoint system. From the numerical point of view, we present a characteristic-Galerkin method for solving the shallow water equations, and an optimization algorithm for the computation of the optimal design variables. Finally, we give numerical results obtained for a standard 10 pools channel.

Flow regulation for water quality restoration in a river section: Modeling and control

This work is devoted to the numerical resolution of an optimal control problem that arises in the management of a reservoir for the remediation of a polluted river section. By using mathematical modeling and optimal control techniques we set the mathematical formulation of the problem (as a hyperbolic optimal control problem with control constraints), and obtain a fully discretized problem. Finally, we propose a gradient-free method to solve it, and present realistic numerical results.

Optimal Shape Design of Wastewater Canals in a Thermal Power Station

Inside the canals of wastewater treatment plants of thermal power stations usually produces in a natural way a deposition of particles in suspension, which causes a change in geometry of the bottom of channel, with the consequent appearance of accumulated sludge and growth of algae and vegetation. This fact may lead to a misfunction of the purification process in the plant. Our main aim focuses on the optimal design of the geometry of such canals to avoid the difficulties derived from these processes. The problem can be formulated as a control-constrained optimal control problem of partial differential equations, and discretized via a characteristics/finite element method. For a simplified case study (canals of rectangular section), theoretical and applicable results are presented.

Optimal Control of Phytoremediation Techniques for Heavy Metals Removal in Shallow Water

In this work we deal with the optimization of different issues related to heavy metals phytoremediation techniques, by combining mathematical modelling, optimal control of partial differential equations and numerical optimization. We introduce a 2D mathematical system of nonlinear partial differential equations modelling the concentrations of heavy metals, algae and nutrients in large waterbodies. We formulate an optimal control problem related to the optimization of the phytoremediation process, and propose a full algorithm for computing the numerical solution of the problem. Finally, we present several numerical results for a realistic problem related to: (i) determining the minimal quantity of algae to be used in the heavy metals remediation process, and (ii) locating the optimal place for such algal mass.

Fishway Optimization Revisited

River fishways are hydraulic structures enabling fish to overcome stream obstructions (for instance, dams in hydroelectric power plants). This paper presents a combination of mathematical modelling and optimal control theory in order to improve the optimal shape design of a fishway. The problem can be formulated within the framework of the optimal control of partial differential equations, approximated by a discrete optimization problem, and solved by using a gradient-type method (the Spectral Projected-Gradient algorithm). Numerical results are shown for a standard real-world situation.

Optimizing Water Quality in a River Section

Since early times, rivers have been not only sources of life but also water discharge receivers (both from industrial and urban origin) from the human settlements on their banks. This fact brings with it that pollutant matter concentration surpasses healthy levels in some sections of the rivers. In our paper, we use mathematical modeling and optimal control theory to simulate one of most common strategies in the pollution reduction of a river section: clear water injection into the channel from a nearby reservoir. In this process of increasing the river flow by controlled releases of water from reservoirs, the main problem consists (once the injection point has been chosen by geophysical reasons) of finding the minimum quantity of water which needs to be injected into the river section in order to purify it to a desired level.

Optimal Control for River Pollution Remediation

The main goal of this work is to use mathematical modelling and numerical optimization to obtain the optimal purification of a polluted section of a river. The most common strategy consists of the injection of clear water from a reservoir in a nearby point. In this process, the main problem consists, once the injection point is selected by geophysical reasons, of finding the minimum quantity of water which is needed to be injected into the river in order to purify it up to a fixed level: this will be the aim of this paper. We formulate this problem as a hyperbolic optimal control problem with control constraints, and deal with its numerical resolution, where a finite elements/finite differences discretization is used, an optimization algorithm is proposed, and computational results are provided.

Fishways Design: An Application of the Optimal Control Theory

The main objective of this work is to present an application of mathematical modelling and optimal control theory to an ecological engineering problem related to preserve and enhance natural stocks of salmon and other fish which migrate between saltwater to freshwater. Particularly, we study the design (first) and the management (second) of a hydraulic structure (fishway) that enable fish to overcome stream obstructions as a dam or a weir. The problems are formulated within the framework of the optimal control of partial differential equations. They are approximated by discrete unconstrained optimization problems and then, solved by using a gradient free method (the Nelder-Mead algorithm). Finally, numerical results are showed for a standard real-world situation.

Mathematical Modelling and Numerical Optimization in the Process of River Pollution Control

Common methods of controlling river pollution include establishing water pollution monitoring stations located along the length of the river. The point where each station is located (sampling point) is of crucial importance and, obviously, depends on the reasons for the sample. Collecting data about pollution at selected points along the river is not the only objective; must also be extrapolated to know the characteristics of the pollution in the entire river. In this work we will deal with the optimal location of sampling points. A mathematical formulation for this problem as well as an efficient algorithm to solve it will be given. Finally, in last sections, we will present numerical results obtained by using this algorithm when applied to a realistic situation in the last sections of a river.