Control of Shallow Water Flows Using an Optimization Procedure and Finite Element Analysis

A new approach using optimization techniques for controlling water flows is proposed in this work. The investigated problem is related to shallow water flows where a given time-evolution of outflow should be determined in order to control water elevation at some region. Typical applications are problems involving the control of movable barriers or water flowing through floodgates to prevent inundation. Usually, this type of problem is solved using gradient-based control techniques which can provide complex solutions that can be difficult to be implemented in practical situations. Here, the shape of the outflow discharge along time is predefined by a curve parametrization and used as design variable of an optimization problem. The shallow water equations are evaluated using the Finite Element Method (FEM). Numerical applications of water height control are presented and the different shapes of water outflow are investigated and discussed. As a result, the present framework can solve optimal flow control problems where an outflow discharge must satisfy a given type of variation along time.