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Dynamical systems-based optimal control of incompressible fluids. (English) Zbl 1081.76016

Summary: For optimal control problems related to fluid flow, the choice of an adequate cost functional for suppression of vortices is of significant importance. In this research we propose a cost functional based on a local dynamical system characterization of vortices. The resulting functional is a non-convex function of the velocity gradient tensor. The resulting optimality system describing first-order necessary optimality conditions is derived, a possible strategy for numerical realization of the optimal control problem is provided, and a numerical feasibility study is conducted.

MSC:

76B75 Flow control and optimization for incompressible inviscid fluids
76M30 Variational methods applied to problems in fluid mechanics
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