Initials Conditions



 
 
 
 
 
 

If we look at the picture ( below ),  we observe precision of initialization is not quite good, and yet we need very good precision to study phenomenon of instabilities. So, we haven't to hope results should be very good.

The precision of initialization is 10E-5.
 
 


(temperature)







Appearance of instability is due to amplification of some perturbations as little as it could be. In order to have better control of establishment of the instability, we decide to impose initial conditions.

comment: term "initial condition" is not really appropriate; indeed, solutions of Rayleigh Benard 's problem ( for epsilon < 20 ) are stationaries, and we don't study transitional period. Therefore, the correct formulation of the corresponding mathematics problem modeling Rayleigh Benard instability needn't initial condition.
 
 
 

We are going to try to impose one, two, three and four rolls :
 

Initial conditions of velocity :

The philosophy of our method is to combine cosines functions with separation of cells ( that FLUENT allows), so that initial conditions should be physically acceptable.

On the one hand, we are going to use command MARK in REGION ( go to ADAPT  )  in order to separate ( with SEPARATE )  edges with middle of the domain to respect condition velocity  which vanish in the four corners of the domain.
 
 


 
 
 
 
 








On the other hand, we define, in central zone, with CUSTOM FIELD FUNCTION,  a velocity with cosines functions  by this way :
 
 









( we determinate order of Vmax by iteration  )
 
 

Boundaries conditions of temperature :

We need to know where we can obtain desired number of rolls. To do that, we use stability curve ( see chapter I). A second curve is interesting, showing zones of stability to obtain desired number of rolls.
So, we can determinate a satisfactory Ra .
 
 

( graph found in 97-98 report .............?)






Study of one roll :
 
 

( initial velocity )
 
 
 
 

(velocity after convergence for Ra=6000)








Two and three rolls establishment is relatively easily, so we don't treat this cases .
 
 
 

In the case of four rolls, we must define four zones in the central area :

The processe is the same than the case of one roll.
 
 








 
 
 

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