MICROSHAPE CONTROL, RIBLETS, AND DRAG MINIMIZATION

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 st...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 73; no. 2; pp. 723 - 740
Main Authors BONNIVARD, MATTHIEU, BUCUR, DORIN
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects
Airy equation
Analysis of PDEs
Applied mathematics
Boundary conditions
Coefficient of friction
Computational fluid dynamics
Drag
Friction
Mathematical functions
Mathematical models
Mathematical problems
Mathematical surfaces
Mathematics
Microstructure
Minimization
Navier Stokes equation
Navier-Stokes equations
Obstacles
Optimization
Stokes flow
Topological theorems
Viscosity
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0036-1399
1095-712X
DOI:10.1137/100814846