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Active control and drag optimization for flow past a circular cylinder. I: Oscillatory cylinder rotation. (English) Zbl 0977.76021

Summary: We investigate computational methods for the active control and drag optimization of incompressible viscous flows past cylinders, using two-dimensional Navier-Stokes equations as the flow model. The computional methodology relies on the following ingredients: space discretization of the Navier-Stokes equations by finite element approximations, time discretization by a second-order-accurate two-step implicit/explicit finite difference scheme, calculation of the cost function gradient by adjoint equation approach, and minimization of the cost function by a quasi-Newton method à la BFGS. The above methods have been applied to boundary control by rotation of the flow around a circular cylinder, and show 30 to 60% drag reduction, compared to the fixed cylinder configuration, for Reynolds numbers in the range from 200 to 1000.

MSC:

76D55 Flow control and optimization for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics

Software:

L-BFGS
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Full Text: DOI

References:

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