Micro-Shape Control, Riblets and Drag Minimization

Matthieu Bonnivard (1) , Dorin Bucur (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 LAMA - Laboratoire de Mathématiques

Relying on the rugosity effect, we analyse the drag minimization problem in relation with the micro-structure of the surface of a given obstacle. We construct a mathematical framework for the optimization problem, prove the existence of an optimal solution by Gamma-convergence arguments and analyse the stability of the drag with respect to the micro-structure. For Stokes flows we justify why rugosity increases the drag, while for Navier-Stokes flows we give some numerical evidence supporting the thesis that adding rugosity on specific regions of the obstacle may contribute to decrease the drag.

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Bonnivard, Dorin Bucur. Micro-Shape Control, Riblets and Drag Minimization. 2013. ⟨hal-00565410v2⟩