Viscous diffusion of multiple vortex system
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:<math> | :<math> | ||
| - | p(x,y,t) = -0.25( \cos 2x | + | p(x,y,t) = -0.25( \cos 2x \cos 2y) e^{-4t/Re} |
</math> | </math> | ||
where <math>u,v</math> are the Cartesian velocity components, <math>p</math> | where <math>u,v</math> are the Cartesian velocity components, <math>p</math> | ||
is the pressure and <math>Re</math> is the [[Reynolds number]]. | is the pressure and <math>Re</math> is the [[Reynolds number]]. | ||
Revision as of 05:54, 12 April 2007
The following analytical solution satisfies the viscous, incompressible
continuity and momentum equations in dimension-less form in the domain 
. The solution is periodic in both 
and
coordinates.
where 
are the Cartesian velocity components, 
is the pressure and 
is the Reynolds number.
