Abstract

We consider the problem of an appropriate choice of a cost functional for vortex reduction for unsteady flows described by the Navier–Stokes equations. This choice is directly related to a physically correct definition of a vortex. Therefore, we discuss different possibilities for the cost functional and analyze the resulting optimal control problems. Moreover, we present an efficient numerical realization of this concept based on space-time finite element discretization and demonstrate its behavior in some numerical experiments. It is demonstrated that the choice of cost functionals has a significant effect on the reduction of vortices.

MSC codes

  1. 35Q30
  2. 76D05
  3. 76D55
  4. 48J20

Keywords

  1. optimal control
  2. vortex reduction
  3. Navier–Stokes equations

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Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 1368 - 1397
ISSN (online): 1095-7138

History

Submitted: 31 May 2005
Accepted: 26 February 2007
Published online: 14 September 2007

MSC codes

  1. 35Q30
  2. 76D05
  3. 76D55
  4. 48J20

Keywords

  1. optimal control
  2. vortex reduction
  3. Navier–Stokes equations

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