Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows

Francesco Ballarin, Andrea Manzoni, Gianluigi Rozza, Sandro Salsa

Risultato della ricerca: Contributo in rivistaArticolo in rivista

22 Citazioni (Scopus)

Abstract

Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.
Lingua originaleEnglish
pagine (da-a)537-563
Numero di pagine27
RivistaJournal of Scientific Computing
Volume60
DOI
Stato di pubblicazionePubblicato - 2014

Keywords

  • Computational fluid dynamics
  • Finite elements method
  • Stokes equations
  • Perturbation of identity
  • Shape optimization
  • Free-form deformations

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