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time stepping in implicit way

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Old   February 26, 2003, 05:34
Default time stepping in implicit way
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varghese
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Hei Gurus,

I read in Fluent Manuals the following statement about the time stepping in implicit way: "The advantage of the fully implicit scheme is that it is unconditionally stable with respect to time step size".

Is it really true?
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Old   February 27, 2003, 02:27
Default Re: time stepping in implicit way
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T. H. Kim
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As you know, the implicit method use the unknown value of next step in calculation. In case of not knowing an initial value, the method is very good. For more details, you must refer to the reference concerning.
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Old   February 27, 2003, 04:35
Default Re: time stepping in implicit way
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Anthony Wachs
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The unconditional stability of implicit scheme for the discretization of the time operator has been proven for a long time in many applied math books.

Therefore for any value of the time step the scheme is expected to be convergent. However, this is not anymore the case when you tackle complex coupled problems. Moreover, unconditional stability does not mean good accuracy of the computed results. If you consider too large time steps, your computed solution will suffer from bad accuracy (lack of precision could sometimes be the main reason of the solution divergence), so watch out !!

If the mathematical analysis of the governing equations does not lead to any criterion on the choice of the time step magnitude, you will have to do it the hard way i.e. by performing numerical experiments.

It depends as well on the time scale of the phenomenon you try to simulate. In this case, the time step magnitude should be less than the physical time scale. Otherwise, you will miss some of the "physics" of your problem.

Hope it could help

Anthony
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Old   February 27, 2003, 08:40
Default Re: time stepping in implicit way
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varghese
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Dear Anthony,

That is really a wonderful answer. I really observed divergence at some time stepping.It perhaps indicates the distortion to the underlying physics of the problem as you have well pointed out.

I am interested to know the type of mathematical analysis that will generate the idea of time stepping suited to a problem, when I use a segregated solver. For coupled solvers, the so called CFL numbers are suggested as the criteria. Does it apply in the case of segregated solver also?

Thanks for the tip!

Varghese
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Old   February 28, 2003, 03:34
Default Re: time stepping in implicit way
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Yong
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CFL numbers is not applied to segregated solver. I agree with Anthony Wachs's idea. I have the same situation in my current work
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