Stokes Problem with Slip Boundary Conditions of Friction Type: Error Analysis of a Four-Field Mixed Variational Formulation

2019 ◽  
Vol 81 (1) ◽  
pp. 312-341
Author(s):  
Mekki Ayadi ◽  
Hela Ayed ◽  
Leonardo Baffico ◽  
Taoufik Sassi
Keyword(s):  
Error Analysis ◽  
Boundary Conditions ◽  
Variational Formulation ◽  
Stokes Problem ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Mixed Variational Formulation

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

The time-dependent Stokes problem with Navier slip boundary conditions on Lp -spaces

Analysis ◽  
2016 ◽  
Vol 36 (4) ◽  
Author(s):  
Hind Al Baba ◽  
Chérif Amrouche ◽  
Ahmed Rejaiba
Keyword(s):  
Boundary Conditions ◽  
Stokes Problem ◽  
Time Dependent ◽  
Slip Boundary Conditions ◽  
Navier Boundary Conditions ◽  
Lp Spaces ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

AbstractThis paper deals with the time-dependent Stokes problem with Navier boundary conditions on

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