On some control problems in fluid mechanics. (English) Zbl 0708.76106

Abergel, F.; Temam, R.

Theor. Comput. Fluid Dyn. 1, No. 6, 303-325 (1990).

Summary: The issue of minimizing turbulence in an evolutionary Navier-Stokes flow is addressed from the point of view of optimal control. We derive theoretical results for various physical situations: distributed control, Bénard-type problems with boundary control, and flow in a channel. For each case that we consider, our results include the formulation of the problem as an optimal control problem and proof of the existence of an optimal control (which is not expected to be unique). Finally, we describe a numerical algorithm based on the gradient method for the corresponding cost function. For readers who are not interested in the mathematical details and the mathematical justifications, a nontechnical description of our results is included.

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
76F99	Turbulence

Keywords:

minimizing turbulence; evolutionary Navier-Stokes flow; optimal control; Bénard-type problems

References:

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