The paper deals with formulation and numerical realization of fluid flow problems with threshold boundary conditions. This means that the slip of the fluid on the boundary may occur only when the shear stress attains a certain bound given a-priori. The mathematical model leads to an inequality type problem. A short comment on the numerical method used for solving such problems and results of several model examples will be presented.

Topics
Numerical methods, Mathematical modeling, Fluid flows, Laminar flows
1.
Ayadi
,
M.
,
Baffico
,
L.
,
Gdoura
,
M. K.
, and
Sassi
,
T.
:
Error estimates for Stokes problem with Tresca friction conditions
,
ESAIM: Mathematical Modelling and Numerical Analysis
, (
5
), pp.
1413
–
1429
,
2014
.
https://doi.org/10.1051/m2an/2014001
Google Scholar
Crossref
Search ADS
 
2.
Bulíček
,
M.
, and
Málek
,
J.
,
2016
. On unsteady internal flows of Bingham fluids subject to threshold slip on the impermeable boundary,
Recent Developments of Mathematical Fluid Mechanics
,
H.
 
Amann
, et al. (eds.), pp.
135
–
156
.
Google Scholar
Crossref
Search ADS
 
3.
Elman
 
H. C.
,
Silvester
 
D. J.
,
Wathen
 
A. J.
:
Finite elements and fast iterative solvers with applications in incompressible fluid dynamics
,
Oxford University Press
,
Oxford
,
2005
.
Google Scholar
 
4.
Fujita
,
H.
,
1994
. A mathematical analysis of motions of viscous incompressible fluid under leak and slip boundary conditions,
RIMS Kokyuroku
,
888
, pp.
199
–
216
.
5.
Koko
 
J.
,
Vectorized Matlab Codes for the Stokes Problem with P1-Bubble/P1 Finite Element
, http://www.isima.fr/∼jkoko/Codes/StokesP1BubbleP1.pdf.
6.
Koko
,
J.
,
2015
.
A MATLAB mesh generator for the two-dimensional finite element method
,
Appl. Math. and Comput.
,
250
, pp.
650
–
664
.
Google Scholar
 
7.
Kučera
,
R.
,
Haslinger
,
J.
,
Šátek
,
V.
, and
Jarošová
,
M.
,
Efficient methods for solving the Stokes problem with slip boundary conditions
,
Math. and Comput. Simul.
, submitted
2015
.
Google Scholar
 
8.
Kučera
,
R.
,
Šátek
,
V.
,
Haslinger
,
J.
,
Fialová
,
S.
, and
Pochylý
,
F.
,
Modelling of Hydrophobic Surfaces by the Stokes Problem with the Stick-Slip Boundary Conditions
,
J. Fluids Eng.
, submited
2016
.
Google Scholar
 
9.
Kučera
 
R.
,
Machalová
 
J.
,
Netuka
 
H.
,
Ženčák
 
P.
:
An interior point algorithm for the minimization arising from 3D contact problems with friction
,
Optimization Methods and Software
 
28
:
6
,
2013
, pp.
1195
–
1217
.
https://doi.org/10.1080/10556788.2012.684352
Google Scholar
Crossref
Search ADS
 
10.
Navier
,
C.L.M.H.
,
Mem.Acad.R.Sci.Inst.France
 
I
(
1823
)
414
.
Google Scholar
 
11.
Pochylý
 
F.
,
Fialová
 
S.
,
Kotek
 
M.
,
Jašíková
 
D.
,
Machů
 
T.
:
Coandã effect with the influence of hydrophobic surface, In
:
Proceedings of the 35th Conference of departments of fluid mechanics and thermomechanics
,
2016
, pp.
77
–
78
.
12.
Pochylý
 
F.
,
Fialová
 
S.
,
Kozubková
 
M.
,
Zavadil
 
L.
:
Assessment of cavitation creation depending on the surface wettability
,
IOP Conference Series: Earth and Environmental Science
, Volume
12
, Issue
1
,
2010
.
Google Scholar
 
This content is only available via PDF.
© 2017 Author(s).
2017
Author(s)
You do not currently have access to this content.