Sediment minimization in canals: An optimal control approach

This work deals with the computational modelling and control of the processes related to the sedimentation of suspended particles in large streams. To analyse this ecological problem, we propose two alternative mathematical models (1D and 2D, respectively) coupling the system for shallow water hydrodynamics with the sediment transport equations. Our main goal is related to establishing the optimal management of a canal (for instance, from a wastewater treatment plant) to avoid the settling of suspended particles and their unwanted effects: channel malfunction, undesired growth of vegetation, etc. So, we formulate the problem as an optimal control problem of partial differential equations, where we consider a set of design variables (the shape of the channel section and the water inflow entering the canal) in order to control the velocity of water and, therefore, the settling of suspended particles. In this first approach to the problem from an environmental/mathematical control viewpoint, in addition to a well-posed mathematical formulation of the problem, we present theoretical and numerical results for a realistic case (interfacing MIKE21 package with our own MATLAB code for Nelder-Mead optimization algorithm).