Simulação numérica e controle ótimo em sistemas de águas rasas

Abstract

In this work, the simulation of flows in shallow water systems is presented in order to contribute to studies of environmental disasters, such as the case of dam break. The numerical simulations are conducted using the Finite Element Method (FEM). The temporal discretization of the equations is developed through the Characteristic-Based Split (CBS) scheme. The optimal control theory is associated with the governing equations of the flow with the objective of searching for an optimal control flow curve that minimizes the objective function, maintaining the water height according to the objective. For this purpose, an evolutionary algorithm SCE-UA (Shuffled Complex Evolution - University of Arizona) is employed, optimizing the parameters of control flow curves, linear and quadratic. Examples of flow in shallow water systems are presented for the application of the methodology, characterizing dam break, wind action and optimal control, comparing the results obtained with the literature. Lastly, a flood set is projected for the Pelotas city, in Rio Grande do Sul, where a numerical simulation of a rupture in the Santa Barbara Dam is performed. Finally, it’s worth emphasizing the results obtained for the dam-break flow characterize an event of harmful consequences, flooding the inhabited region by up to 3 meters in approximately 30 minutes.