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Old   November 12, 2005, 16:15
Default Unsteady timestep
  #1
Unsteady Guy
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hello; iam a new CFD user; i have just a quick question for solver that uses fully implicit scheme for transient simulations; how can i specify timestep; i know that the timstep should be equal or smaller than certain number, depending on the length-scale and velocity scale; is the length-scale the distance between elements or is it related to the geomatry of the problem??

thank you
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Old   November 12, 2005, 17:15
Default Re: Unsteady time step
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Renato
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You must be talking about the Courant number, or CFL. The CFL number is a kind of measure for the solution mobility and is expressed by:

CFL = dt * ||u|| / he

where dt is the time step, ||u|| is the norm of the velocity and he is the element length.

This relationship tell you how many elements your solution will advance at each time step.

Furthermore, as you can see, the CFL condition is defined for each element in your mesh and is advisable keeping it less than 1 for a good time accurate solution.

You could have an idea for your solution time step by taking the minor element size from your mesh and estimating the time step according to CFL condition.

It's easy to go deepest in this subject by googling for "courant number" or "CFL condition" keywords or in any good CFD book.

Regards

Renato.

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Old   November 12, 2005, 18:11
Default Re: Unsteady time step
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Unsteady Guy
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thank you, i will look into it

however, is there a general criterea that takes into consideration the velocity and length referenace scale (not the element length) to compute the maximum timestep should be
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Old   November 12, 2005, 18:43
Default Re: Unsteady time step
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Renato
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Hmmmm, let me state a very simple example:

imagine you have a model with 10 length units in the flow direction and along this direction you divide your domain in 10 elements, so you will have 1 length unit per element. If you set the inlet velocity to 1 [L/T] you will have:

dt = he * CFL / ||u||

so, your time step shouldn't be more than 1 ;o)

Of course, it's a very naive approach considering a structured mesh and elements uniformly distributed but it's a very easy and straightforward way to get some idea...

Regards

Renato.
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Old   November 13, 2005, 22:02
Default Re: Unsteady timestep
  #5
Praveen. C
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There are two time scales in an unsteady flow. One coming from the cfl condition and another from the unsteady flow. The time step you use must be smaller than both of these.
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