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January 15, 2004, 15:12 
Why dualtime stepping?

#1 
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Hi all,
I have a question on "dualtime stepping" technique. Simply, why? What is the advantage? You solve a steadystate problem at every realtime step, which can take very long. Yes, you can use preconditioning or multigrid etc, but what is the point of creating a steadystate problem and solving that. I really want to know the reason why dualtime stepping has its place. Thank you Dave 

January 15, 2004, 22:16 
Re: Why dualtime stepping?

#2 
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Dual timestepping is useful for implicit, unsteady calculations. See the following http://aerocomlab.stanford.edu/Pape...afosr.2003.pdf


January 16, 2004, 07:55 
Re: Why dualtime stepping?

#3 
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Thanks Praveen, I have just read page 17 of Jameson's slides.
As I understand, in order to use a much larger time step dt in the time marching, an implicit scheme is employed. However, the implicit formulation i.e. equation (4) is difficult to solve. In order to solve the implicit equation (4) to obtain w(n+1), an artificial time t* is introduced and w(n+1) is treated as a steady state solution of the equation (5). In order to solve the equation (5), an explicit artificial time marching is used, How large the artificial time step dt* can be used depends on the stability of equation (5). The time accuracy of the original problem depends on the real time step dt. Please correct me if my understanding is wrong. Li Yang 

January 18, 2004, 06:53 
Re: Why dualtime stepping?

#4 
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Treat flow solution of t+1 as the steadystate, from a initial flow solution at t, requires several (<5) subiterations to achived the required time accuracy. That is the hoped performance of dual time stepping. Why use dual time stepping? some numerical schemes contain factorization error, timeaccuracy is not exactedly meeted if solved once. However, The merit of dual time steeping depends on the subiteration procedure. One may naively think it needs only a few subierations from T to T+1 as the two flow fields are so close. But things are not so simple, especillay coupled with nonlinear boundary condition. A residual drop of 12 order is quickly reached, but further 45 orders reduction in residual is very difficult to attain within acceptable iteration numbers. SO you need develop good preconditioning iterative proceudre when using dualtime steeping.


January 21, 2004, 11:29 
Re: Why dualtime stepping?

#5 
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ok, the explanation in the Jameson's presentation was the mathematical explanation. Can anyone explain me what is the physics behind it? why does the duel time stepping solves it faster and why it is required? might look like a dumb questions to some people but its still a puzzle for me.
J 

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