# Time step size????

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 March 22, 2009, 23:02 Time step size???? #1 Member   MrFluent Join Date: Mar 2009 Posts: 33 Rep Power: 17 I am wondering about one question. Lets say i have a cartesian mesh domain, whose smallest cell size is 1E-4meters. 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 22, 2009, 23:25
#2
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Prakash Ayappan
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Quote:
 Originally Posted by mr_fluent I am wondering about one question. Lets say i have a cartesian mesh domain, whose smallest cell size is 1E-4meters. 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.
For that you have to integrate the momentum eqn. And make sure the constant co-efficient term to be positve. A rough estimate will be (for 2D case energy eqn)
time step = (del X)^2/(Alpha). where alpha is the diffusivity.

March 22, 2009, 23:51
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MrFluent
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Quote:
 Originally Posted by technocrat.prakash For that you have to integrate the momentum eqn. And make sure the constant co-efficient term to be positve. A rough estimate will be (for 2D case energy eqn) time step = (del X)^2/(Alpha). where alpha is the diffusivity.

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, 02:55 #4 Senior Member     p ding Join Date: Mar 2009 Posts: 427 Rep Power: 19 i prefer a full implicit method, so we do not have the problem about time step size

 March 23, 2009, 03:05 Courant criteria #5 New Member   Join Date: Mar 2009 Posts: 4 Rep Power: 17 Do you have to consider the Courant criteria for this case?

March 23, 2009, 03:05
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MrFluent
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 Originally Posted by ztdep i prefer a full implicit method, so we do not have the problem about time step size

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).

 March 23, 2009, 05:06 #7 Member   MrFluent Join Date: Mar 2009 Posts: 33 Rep Power: 17 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, 05:25 #8 New Member   Prakash Ayappan Join Date: Mar 2009 Posts: 25 Rep Power: 17 Good. Keep Going.

March 23, 2009, 07:20
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p ding
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Quote:
 Originally Posted by mr_fluent 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.
i do not think you can reduce the time greatly, since the explicit method has the limitation in the time step.

March 23, 2009, 07:48
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MrFluent
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Quote:
 Originally Posted by ztdep i do not think you can reduce the time greatly, since the explicit method has the limitation in the time step.
Actually i am already supposed to use time step sizes smaller than 1e-4 or so.

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