A Continuous Adjoint Approach to Shape Optimization for Navier Stokes Flow

  • Christian Brandenburg
  • Florian Lindemann
  • Michael Ulbrich
  • Stefan Ulbrich
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 158)

Abstract

In this paper we present an approach to shape optimization which is based on continuous adjoint computations. If the exact discrete adjoint equation is used, the resulting formula yields the exact discrete reduced gradient. We first introduce the adjoint-based shape derivative computation in a Banach space setting. This method is then applied to the instationary Navier-Stokes equations. Finally, we give some numerical results.

Mathematics Subject Classification (2000)

Primary 76D55 Secondary 49K20 

Keywords

Shape optimization Navier-Stokes equations PDE-constrained optimization 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Christian Brandenburg
    • 1
  • Florian Lindemann
    • 2
  • Michael Ulbrich
    • 2
  • Stefan Ulbrich
    • 1
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadt
  2. 2.Lehrstuhl für Mathematische Optimierung Zentrum Mathematik, M1TU MünchenGarching bei München

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