Application of an adjoint-based optimization procedure for the optimal control of internal boundary conditions in the shallow water equations

Abstract

ABSTRACTThe shallow water equations have been extensively studied and used to model unsteady open channel flows in different applications. They belong to the category of hyperbolic partial differential equations and their treatment has recently been benefited from many numerical contributions leading to robust, accurate and well-balanced solutions. The correct formulation of external and internal boundary conditions is required to achieve a useful model in practical application. Control of internal boundary conditions may be useful in water distribution facilities. Therefore, development of a control strategy based on the fully dynamical mathematical model becomes attractive and justified. This work is devoted to the implementation of an adjoint based sensitivity analysis for the control of sluice gates in open-channel flow, formulated as internal boundary conditions. This is one of the most complex tasks in multiple regulated water delivery situations. Based on gradient method optimizers, the control of the whole channel to satisfy different requirements at several points of the channel is discussed. One of the achievements in this work is that the whole optimization process is performed two orders of magnitude faster than in real time. Moreover, the numerical results show this promising technique is a feasible way to obtain a robust and efficient control method.