[Wrf-users] CFL criterion - general question

[Anders Nottrott]

Hi All,

The maximum value of the CFL number is set by the 
Courant-Friedrichs-Lewy condition (see WRF Description, Section 3.3 
Stability Constraints). It is a necessary condition for the convergence 
of the finite difference integration schemes.

Generally CFL = u_i*dt/dx_i, where u_i is the maximum velocity in the 
ith direction, dt is the timestep and  dx_i is the grid spacing in the 
ith direction. For a simple 1D advection equation with an explicit 
solver the requirement is CFL < 1 everywhere in the domain. The limiting 
value is different for other equations and higher order finite 
difference schemes.

If you get an error message saying that the CFL was violated you should 
consider the solution associated with that simulation to be spurious. To 
resolve this problem you can either reduce dt (which increases the 
computation time) or you can increase dx (which reduces resolution) and 
rerun the simulation. Keep in mind that u_i is the maximum velocity in 
the ith direction so a large velocity event at even one grid point can 
cause you simulation to "blow up" in just a couple of time steps. Thus 
it is important to consider the CFL in three dimensions and then allow 
some small factor of safety in the design of dt or dx.

Regards,

Anders


-- 
Anders Nottrott
/PhD Student, Mechanical and Environmental Engineering/
University of California, San Diego
Department of Mechanical and Aerospace Engineering
Website: solar.ucsd.edu/nottrott

On 11/1/2012 11:37 AM, Kevin Matthew Nuss wrote:
> Hi Elena,
>
> I have had the same thing happen. I don't know exactly how that 
> affects the results, so when it has happened to me, I did not trust 
> the results.
>
> Yes, reducing the time step is the standard way to avoid CFL errors. 
> There are some alternatives like using restart files: when CFLs 
> appear, stop, go back a little way in time, use small time steps for a 
> while, stop and continue forward using the larger timesteps. That is 
> mostly done for very long runs like climate downscaling when it is not 
> practical to use small timesteps for an entire run.
>
> If CFLs always appear at the same coordinates such as a mountain peak, 
> EPSSM can be adjusted or the grid changed.
>
> If you need more information and detail about what I do to avoid CFL 
> errors, I have some on my website: http://www.nusculus.com/wrf-errors
>
> I don't claim to be an expert; I have simply suffered through a lot of 
> bad WRF runs.
>
> But most people just keep reducing the time step until the CFL errors 
> go away.
>
> Kevin
>
> On Wed, Oct 31, 2012 at 11:51 PM, Elena Maria Pison San Pedro 
> <emp at dhi.com.sg <mailto:emp at dhi.com.sg>> wrote:
>
>     Hello,
>
>     I've remarked that sometimes when I run a simulation (WRF3.4) I
>     got messages saying " x points exceeded cfl=2 at time..." _but the
>     simulation run to completion_.
>
>     How can this affect the results? What can I do to solve this
>     instabilities, run a higher time step?
>
>     Thanks a lot in advance!
>
>     Best regards,
>
>     Elena
>
>     Elena Pison San Pedro
>
>     M.Sc. in Atmospheric Sciences
>
>
>     Description:
>     C:\Users\mmc\AppData\Roaming\Microsoft\Signatures\dhi_logo.gif
>
>     DHI-NTU Research Centre and Education Hub,
>
>     DHI Water & Environment (S) Pte Ltd
>
>     1 Clean Tech Loop
>
>     #03-05 CleanTech One
>
>     Singapore 637141
>
>
>
>
>
>
>
>
>
>
>     Tel:
>
>     	
>
>     	
>
>     +65-6777-6330 <tel:%2B65-6777-6330>
>
>     emp at dhi.com.sg <mailto:emp at dhi.com.sg>
>
>     www.dhigroup.com <http://www.dhigroup.com/>
>
>
>     _______________________________________________
>     Wrf-users mailing list
>     Wrf-users at ucar.edu <mailto:Wrf-users at ucar.edu>
>     http://mailman.ucar.edu/mailman/listinfo/wrf-users
>
>
>
>
> _______________________________________________
> Wrf-users mailing list
> Wrf-users at ucar.edu
> http://mailman.ucar.edu/mailman/listinfo/wrf-users
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://mailman.ucar.edu/pipermail/wrf-users/attachments/20121101/42a4c6e7/attachment-0001.html 
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: image/jpeg
Size: 141589 bytes
Desc: not available
Url : http://mailman.ucar.edu/pipermail/wrf-users/attachments/20121101/42a4c6e7/attachment-0001.jpe 
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: image/gif
Size: 2148 bytes
Desc: not available
Url : http://mailman.ucar.edu/pipermail/wrf-users/attachments/20121101/42a4c6e7/attachment-0001.gif