2013/01/01 by Matthieu Bonnivard, Dorin Bucur
Chemical Engineering · Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Computer science #Convergence (economics) #Drag #Economics #Mathematical analysis #Mathematical optimization #Mathematics #Mechanics #Minification #Obstacle #Physics #Rheology and Fluid Dynamics Studies #Rugosity
paper · doi:10.1137/100814846
crossref issued 2013/01/01 · crossref published 2013/01/01 · crossref published-print 2013/01/01 · openalex publication_date 2013/01/01 · crossref created 2013/03/19 · crossref deposited 2022/02/11 · openalex created_date 2025/10/10 · crossref indexed 2026/07/29 · openalex updated_date 2026/07/30
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 Γ-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.