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March 23, 2009, 00:02 
Time step size????

#1 
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MrFluent
Join Date: Mar 2009
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I am wondering about one question.
Lets say i have a cartesian mesh domain, whose smallest cell size is 1E4meters. And if i have maximum velocity in domain aroun say 100m/s. And in momentum equations if i am treating convection terms as explicit but diffusion terms fully implicit. How do i decide what maximum time step size i could use. Is there any pointers where i could find a definitive formula to use in this case. 

March 23, 2009, 00:25 

#2  
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Prakash Ayappan
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Quote:
time step = (del X)^2/(Alpha). where alpha is the diffusivity. 

March 23, 2009, 00:51 

#3  
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MrFluent
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Quote:
Thanks for replying. The reason for my question was that is there any other criteria that also should be taken care of. My momentum term diagonal matrix is all positive for two reasons. By treating convection term explicit, i only have diffusion terms in matrix, they produce positive diagonal plus its a transient case of there is contribution from 1/delt_t too. 

March 23, 2009, 03:55 

#4 
Senior Member

i prefer a full implicit method, so we do not have the problem about time step size


March 23, 2009, 04:05 
Courant criteria

#5 
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Do you have to consider the Courant criteria for this case?


March 23, 2009, 04:05 

#6  
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MrFluent
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Quote:
Actually i also prefer but since i have to use a very small time step, irrespective of method i use, i was thinking if i could ditch convection term then i am all left with diffusional terms. Now if i only take diffusional terms, my matrix would be more of less similar for u,v,w equations. If this is the case i could reduce operation count greatly. So whole idea was if i am forced to use small step could i make some shortcut. But it seems i might have to go with implicit, because in my case del_x/umax is too small, (smaller than time step i have to use). thanks for replying though. 

March 23, 2009, 06:06 

#7 
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MrFluent
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thanks guys, i finally ended up making it fully implicit and in almost similar calculation efficiency if it were only diffusional matrix.
I checked it and its working fine. Thanks again. 

March 23, 2009, 06:25 

#8 
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Prakash Ayappan
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Good. Keep Going.


March 23, 2009, 08:20 

#9  
Senior Member

Quote:


March 23, 2009, 08:48 

#10  
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MrFluent
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Quote:
Anyway i was trying to implement approaximate factorization as kim and moin used in their paper (1984 dns paper). For that i was supposed to solve them by tdma. But since i am solving by tdma, keeping convection terms in solver matrix does not really add anything to calculation time. So i did that. And now it is fully implicit and working well. 

Tags 
courant number, time step size 
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