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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