From Euler and Navier–Stokes equations to shallow waters by asymptotic analysis

2007 ◽  
Vol 38 (6) ◽  
pp. 399-409 ◽  
Author(s):  
J.M. Rodríguez ◽  
R. Taboada-Vázquez
Keyword(s):  
Asymptotic Analysis ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Shallow Waters ◽  
Navier Stokes Equations

ON THE ASYMPTOTIC ANALYSIS OF THE BGK MODEL TOWARD THE INCOMPRESSIBLE LINEAR NAVIER–STOKES EQUATION

2010 ◽  
Vol 20 (08) ◽  
pp. 1299-1318 ◽  
Author(s):  
A. BELLOUQUID
Keyword(s):  
Asymptotic Analysis ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Uniqueness Theorems ◽  
Bgk Model ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stokes Systems ◽  
Global Strong Solutions

This paper deals with the analysis of the asymptotic limit for BGK model to the linearized Navier–Stokes equations when the Knudsen number ε tends to zero. The uniform (in ε) existence of global strong solutions and uniqueness theorems are proved for regular initial fluctuations. As ε tends to zero, the solution of BGK model converges strongly to the solution of the linearized Navier–Stokes systems. The validity of the BGK model is critically analyzed.

Quantities which define conically self-similar free-vortex solutions to the Navier–Stokes equations uniquely

2001 ◽  
Vol 438 ◽  
pp. 159-181 ◽  
Author(s):  
CARL FREDRIK STEIN
Keyword(s):  
Asymptotic Analysis ◽  
Tangential Stress ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Opening Angle ◽  
Bounding Surface ◽  
Free Vortex ◽  
Navier Stokes Equations ◽  
Vortex Solutions ◽  
Self Similar

It is proved that if, in addition to the opening angle of the bounding conical streamsurface and the circulation thereon, one of the radial velocity, the radial tangential stress or the pressure on the bounding streamsurface is given, then a conically self-similar free-vortex solution is uniquely determined in the entire conical domain. In addition, it is shown that for ows inside a cone the same conclusion holds for the Yih et al. (1982) parameter T, but for exterior flows it is shown numerically that non-uniqueness may occur. For given values of the opening angle of the bounding conical streamsurface and the circulation thereon the asymptotic analysis of Shtern & Hussain (1996) is applied to obtain asymptotic formulae which interrelate the opening angle of the cone along which the jet fans out and the radial tangential stress on the bounding surface. A striking property of these formulae is that the opening angle of the cone along which the jet fans out is independent of the value of the viscosity as long as it is small enough for the first-order asymptotic expressions to apply. However, these formulae are shown to be inaccurate for moderate values of the ratio of the circulation at the bounding surface and the viscosity. To amend this shortcoming, an alternative, more accurate, asymptotic analysis is developed to derive second-order correction terms, which considerably improve the accuracy.

Asymptotic analysis of the navier-stokes equations

1983 ◽  
Vol 9 (1-2) ◽  
pp. 157-188 ◽  
Author(s):  
C. Foias ◽  
O.P. Manley ◽  
R. Temam ◽  
Y.M. Treve
Keyword(s):  
Asymptotic Analysis ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
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