Microshape Control, Riblets, and Drag Minimization

• Autores: Matthieu Bonnivard, Dorin Bucur
• Localización: Siam journal on applied mathematics, ISSN 0036-1399, Vol. 73, Nº 2, 2013, págs. 723-740
• Idioma: inglés
• DOI: 10.1137/100814846
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• Resumen

  • Relying on the rugosity effect, we analyse the drag minimization problem in relation to the microstructure 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 analyze the stability of the drag with respect to the microstructure. 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 decreasing the drag.