On the Navier-Stokes equations in non-cylindrical domains: On the existence and regularity

1988 ◽  
Vol 199 (2) ◽  
pp. 153-170 ◽  
Author(s):  
Rodolfo Salvi
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cylindrical Domains

scholarly journals Numerical simulation of supersquare patterns in Faraday waves

2015 ◽  
Vol 772 ◽  
Author(s):  
L. Kahouadji ◽  
N. Périnet ◽  
L. S. Tuckerman ◽  
S. Shin ◽  
J. Chergui ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Outer Wall ◽  
Wave Pattern ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Critical Wavelength ◽  
Characteristic Wavelength ◽  
Cylindrical Domains ◽  
Lagrangian Tracking

We report the first simulations of the Faraday instability using the full three-dimensional Navier–Stokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid front-tracking/level-set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. Simulations performed in square and cylindrical domains yield complex patterns. In particular, a superlattice-like pattern similar to those of Douady & Fauve (Europhys. Lett., vol. 6, 1988, pp. 221–226) and Douady (J. Fluid Mech., vol. 221, 1990, pp. 383–409) is observed. The pattern consists of the superposition of two square superlattices. We conjecture that such patterns are widespread if the square container is large compared with the critical wavelength. In the cylinder, pentagonal cells near the outer wall allow a square-wave pattern to be accommodated in the centre.

On a Problem Connected with Navier-stokes Equations in Non Cylindrical Domains

2005 ◽  
Vol 1 (1) ◽  
pp. 78-85
Author(s):  
J. Limaco ◽  
S.B. de Menezes ◽  
C. Vaz ◽  
J.F Montenegro
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cylindrical Domains
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