Dual strategies for solving the Stokes problem with stick–slip boundary conditions in 3D

2020 ◽  
Author(s):  
Jaroslav Haslinger ◽  
Radek Kučera ◽  
Taoufik Sassi ◽  
Václav Šátek
Keyword(s):  
Boundary Conditions ◽  
Stokes Problem ◽  
Slip Boundary Conditions ◽  
Stick Slip ◽  
Slip Boundary

Linearized no-slip boundary conditions at a rough surface

2013 ◽  
Vol 737 ◽  
pp. 349-367 ◽  
Author(s):  
Paolo Luchini
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Solid Wall ◽  
Stokes Problem ◽  
Far Field ◽  
Slip Boundary Conditions ◽  
Transition Prediction ◽  
Slip Boundary ◽  
Flow Problems ◽  
Field Behaviour

AbstractLinearized boundary conditions are a commonplace numerical tool in any flow problems where the solid wall is nominally flat but the effects of small waviness or roughness are being investigated. Typical examples are stability problems in the presence of undulated walls or interfaces, and receptivity problems in aerodynamic transition prediction or turbulent flow control. However, to pose such problems properly, solutions in two mathematical distinguished limits have to be considered: a shallow-roughness limit, where not only roughness height but also its aspect ratio becomes smaller and smaller, and a small-roughness limit, where the size of the roughness tends to zero but its aspect ratio need not. Here a connection between the two solutions is established through an analysis of their far-field behaviour. As a result, the effect of the surface in the small-roughness limit, obtained from a numerical solution of the Stokes problem, can be recast as an equivalent shallow-roughness linearized boundary condition corrected by a suitable protrusion coefficient (related to the protrusion height used years ago in the study of riblets) and a proximity coefficient, accounting for the interference between multiple protrusions in a periodic array. Numerically computed plots and interpolation formulas of such correction coefficients are provided.

Efficient methods for solving the Stokes problem with slip boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 114-124 ◽  
Author(s):  
Radek Kučera ◽  
Jaroslav Haslinger ◽  
Václav Šátek ◽  
Marta Jarošová
Keyword(s):  
Boundary Conditions ◽  
Stokes Problem ◽  
Slip Boundary Conditions ◽  
Slip Boundary
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