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December 22, 2004, 09:37 
local timestep

#1 
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Hi everybody,
I have just discovered the "local timestep", that is using a timestep varying in space, and I have some questions about it, it would be nice if some of you could help me. .Does it have something to do with "fractional step"? .Will a result of a local timestep computation be just like the one of a steady state computation? .Are there some tricks or things I should care about when using this option? like special care for convergence or so. .Do you have any comment about it? Thanks 

December 22, 2004, 10:46 
Re: local timestep

#2 
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Hi,
Local time steping is one of a bunch of ways of accelerating convergence of numerical simulations. It is mainly used for obtaining steadystate solutions, since the physical meaning of the time step is lost as each cell can advance differently in time. If you got a converged solution with local time steping, then you should theoretically have a steadystate solution. What you shouldn't expect is to have correct transient solutions, since you've lost the physical meaning of time advance. (There is also a way to use local time steping to transient solution, but this is an advanced topic.) I'm not so sure about what you mean exactly with "fractional step", but I'd guess this has something to do with an effort of people from Finite Elements trying to adapt the local time step concept to their formulation. They apparently cannot do this in a straightfoward manner and so they invented a workaround for it. A very gross idea is that the cells that can advance more in time, receive more fractions of a given time step. When using local time steping, you must probably define a characteristic length scale to the cell (such as in the CFL number definition). There is not a precise definition for that length and you should take care about choosing your own. And when someone says, "I use CFL of that much", you should ask, "in which characteristic length is this based?" I would recommend reading the chapter on this stuff in Hirsch. Best regards, Biga 

December 22, 2004, 17:57 
Re: local timestep

#3 
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Thank you very much!
by fractional step, I was refering to a previous message in this forum :"Annie , Wed, 15 Dec 2004, 1:58 a.m." I guess I just have to find that bok from Hirsch now. 

December 23, 2004, 11:24 
Re: local timestep

#4 
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Yes! I strongly recommend reading Hirsch... =)
About fractional step, I really got it wrong. It doesn't have nothing to do with what I said. It's all about how to integrate incompressible flows in time, which have decoupled momentum and pressure equations. Here is an article on that subject I've just googled: http://anziamj.austms.org.au/V45/CTAC2003/Armf/Armf.pdf Regards, Biga 

December 23, 2004, 20:10 
Re: local timestep

#5 
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When people use the words Fractional Step, most often, they are refering to the fact that different terms of the governing equation are treated separately. This is what I understand from the literature, please correct me if I am wrong.
E.g. ADI (for parabolic equations) is the simplest form of fractional stepping  take a half step in X ignoring any evolution in Y and then take another half step in Y ignoring any evolution in X. Do this without losing consistency, and do it implicitly, giving the required stability. E.g. Often (e.g. in spectral methods) people integrate the convective term in a half step and the remaining (pressure, viscous) terms in another half step. E.g. Some others use a multistep, Adamstype, method and alternately evaluate different terms using previous data. 

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