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 mr_fluent March 23, 2009 00:02

Time step size????

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.

 technocrat.prakash March 23, 2009 00:25

Quote:
 Originally Posted by mr_fluent (Post 210327) 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.

 mr_fluent March 23, 2009 00:51

Quote:
 Originally Posted by technocrat.prakash (Post 210334) 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.

 ztdep March 23, 2009 03:55

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

 Hochola March 23, 2009 04:05

Courant criteria

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

 mr_fluent March 23, 2009 04:05

Quote:
 Originally Posted by ztdep (Post 210354) 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.

:D

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).

 mr_fluent March 23, 2009 06:06

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.

 technocrat.prakash March 23, 2009 06:25

Good. Keep Going.

 ztdep March 23, 2009 08:20

Quote:
 Originally Posted by mr_fluent (Post 210361) 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. :D 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.

 mr_fluent March 23, 2009 08:48

Quote:
 Originally Posted by ztdep (Post 210416) 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.

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