Geometrical shape optimization in fluid mechanics using FreeFem++

Charles Dapogny (1) , Pascal Frey (2) , Florian Omnès (2) , Yannick Privat (2) , Florian Omnès (2)

1 CVGI - Calcul des Variations, Géométrie, Image
2 LJLL - Laboratoire Jacques-Louis Lions

In this article, we present simple and robust numerical methods for two-dimensional geometrical shape optimization problems, in the context of viscous flows driven by the stationary Navier-Stokes equations at low Reynolds number. The salient features of our algorithm are exposed with an educational purpose; in particular, the numerical resolution of the nonlinear stationary Navier-Stokes system, the Hadamard boundary variation method for calculating the sensitivity of the minimized function of the domain, and the mesh update strategy are carefully described. Several pedagogical examples are discussed. The corresponding programs are written in the FreeFem++ environment; they are freely available and can easily be elaborated upon to deal with different, or more complex physical situations.

Domaines: Equations aux dérivées partielles [math.AP]

Charles Dapogny, Pascal Frey, Florian Omnès, Yannick Privat, Florian Omnès. Geometrical shape optimization in fluid mechanics using FreeFem++. Structural and Multidisciplinary Optimization, 2018, 58, pp.2761-2788. ⟨10.1007/s00158-018-2023-2⟩. ⟨hal-01481707v2⟩