Abstract
An optimal flow control methodology based on adjoint sensitivity analysis for controlling nonlinear open channel flows with complex geometries is presented. The adjoint equations, derived from the nonlinear Saint-Venant equations, are generally capable of evaluating the time-dependent sensitivities with respect to a variety of control variables under complex flow conditions and cross-section shapes. The internal boundary conditions of the adjoint equations at a confluence (junction) derived by the variational approach make the flow control model applicable to solve optimal flow control problems in a channel network over a watershed. As a result, an optimal flow control software package has been developed, in which two basic modules, i.e., a hydrodynamic module and a bound constrained optimization module using the limited-memory quasi-Newton algorithm, are integrated. The effectiveness and applicability of this integrated optimal control tool are demonstrated thoroughly by implementing flood diversion controls in rivers, from one reach with a single or multiple floodgates (with or without constraints), to a channel network with multiple floodgates. This new optimal flow control model can be generally applied to make optimal decisions in real-time flood control and water resource management in a watershed.
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