Michael Hinze, Karl Kunisch:

Control strategies for fluid flows - optimal versus suboptimal control

Optimal and instantaneous control strategies for fluid flows governed by the Navier-Stokes equation (NSE) are investigated. Control laws derived from instantaneous optimization are compared to those obtained by optimal control. Although instantaneous control is a suboptimal strategy its numerical implementation yields excellent results compared to optimal control applied to the same problem. Furthermore, the numerical expense of instantaneous control can be compared to that of one forward and one backward solve in the optimality system of the optimization problem. Numerical examples for instantaneous and optimal control are given. The focus here is on comparing optimal and suboptimal control strategies with regard to cost reduction and numerical expense for backward facing step flows.

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