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Old   May 22, 2008, 07:11
Default Implicit time-stepping
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I wonder what the physical meaning is of using large time-steps in a simulation. I.e. using time-steps that violates the courant number. I understand that the transients of the flow can not be described correctly in such a simulation but is it possible to draw any form of conclusion from a flow field before it has reached some sort of steady state in such a case?
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Old   May 22, 2008, 09:06
Default Re: Implicit time-stepping
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In CFD simulations, time step we choose depends on two factor one is physics and other is numerics.

It is advisable to use Explicit procedures when the time scales associated with the physics are very small and to resolve this physics we require to march with smaller time steppings. Again how small should be the time step ??, If your time step associated with numerics (that is using CFL criteria) is comparable with the time scales asociated with the physics of the problem then we can use explicit procedures to get your solution.

On other hand, Implicit procedures are unconditionally stable (for a linear problem) and allows us to take large time scales. So if your time scales asociated with the physics are sufficiently large, in this case there is no point in using small time steps with explicit procedures as there is not significient physics happenning in that small time step and it is wise to use larger time steps to march towards the final solution (steady or unsteady) using Implict procedures.

Thats the reason why when we solve a steady state problem initially we choose less CFL (ie, less time step) to capture the evolution of the final solution form the initial solution and later gradually when the solution approches towards the final state (when the gradiants of the solutions are less) we take very large time steps to reach the steady state even faster.

So answering Sara's question in one sentence, Courant number condition is a limit on the stability of the numerical algorithim not on the actual physics ONLY IF time scales involved are very large in your problem, capturing the sufficient physics is governed by the time step you choose which may or may not be permitted by your algoritham (explicit wont while Implict permits).

Thats why CFD is all about " PHYSICS + NUMERICS "........

Thanks, Vinayender.
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