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August 15, 2010, 10:30 
CFL number in steady simulations

#1 
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Roland
Join Date: Jul 2010
Posts: 8
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as i understood, the CFL number limits the time step in an unsteady simulation. But how can the CFL number affect a steady simulation?
From experience I know that a higher CFL number leads to faster convergence, but is less stable, so the CFL number must be somehow used by the solver, even in a steady simulation. i would appreciate any enlightenment 

August 18, 2010, 01:16 

#2 
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Shyam
Join Date: Apr 2009
Posts: 29
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The CFL number is a scaling factor to limit the time step size. For transient problem, this time step size is controlled by the element size and the wave speed for stability purpose. The time step size should also be respected to maintain temporal accuracy of the solution.
Now, for steady state problems, the CFL limit is still essential for maintaining stability of the solver. But, since the time accuracy is not needed, one can choose unphysical time stepping methods. Some of them are: Local time stepping, multigrid, GMRES class of methods etc., which accelerate the convergence of the solution to steady state. 

August 19, 2010, 09:28 

#3 
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Freddie Sizer
Join Date: Apr 2009
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Rol, would you by any chance be using an implicit solver?
If you are then I don't think the CFL condition applies in the way that you are probably thinking. i.e explicitly. In an explicit solver the cfl condition is everything, however with implicit solvers there is an extra equation that needs to be solved, which somehow means that cfl numbers can be much higher leading to the faster convergence you mentioned. Can anyone on here describe how to estimate the cfl number to use in implicit codes? 

August 20, 2010, 05:08 

#4 
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Roland
Join Date: Jul 2010
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yes, sorry, i should have mentioned that we use an implicid solver. i can not tell you how to estimate be cfl number for steady simulations, but i can tell you that we use cfl numbers from 100 to 0.1, 100 for fast convergence, 1 for the first 100 iterations. i always let my simulations converge with a final cfl number between 10 and 1. I have seen similar values for another code, so i guess that are standard values.
could you give a reference to that extra equation, wher the cfl number occurs? 

August 20, 2010, 09:17 

#5 
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Freddie Sizer
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the simplest and best description is on wikipedia under explicit and implicit methods:
http://en.wikipedia.org/wiki/Explici...plicit_methods It's just the difference in the way that the differential equations are numerically solved, so nothing to complex, although when applied to navier stokes there is an extra computation to solve each ode. That last bit confuses me a little bit because you would think this extra computation would increase convergence time! Some more reading required!....... 

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