Influence of the initialisation

 
 

In the unsteady case the initialisation is a factor that determines which solution the calculus is going to converge towards, which states it will go trough. We tried to control the rolls production by imposing initial conditions. To study the influence of the initialisation we set the X-velocity to a value that depends of the Y coordinate:
 

 

Vx=0.01cos(200 PI Y)


 
 

Then we calculated the unsteady flow and observed the intermediates states.


 
 
 


 
 
 

Vy=0.01sin(400 Pi X)

We can notice that after a quick evolution in the firsts time steps, with four rolls, the solution stabilises at an intermediate state with three rolls. In the end, the solution turns unstable before converging towards the steady solution with two rolls. This unstable state with three rolls is possible because the Rayleigh number is equal to 2500 which allows multiple wave length.
 

 

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