## stability criterion

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nmichelet
Posts: 31
Joined: Fri Oct 02, 2015 2:24 pm
Location: Cerema

### stability criterion

Hello,
I have a question about the stability criterion in ROMS. I have found that there is a CFL criterion which is calculate with 2D time step like :

CFL = sqrt(gh)*Delta_t2d*sqrt(Delta_x^-2+Delta_y^-2)

And this CFL has to be lower than 1/2. But is there a stability criterion which is calculated with 3D time step? If yes, what is it's formulation?

Thanks

lfparejar
Posts: 12
Joined: Sat Oct 05, 2013 5:21 am
Location: Rutgers University

### Re: stability criterion

As far as I know, the CFL criterion (or C) is calculated for u, v and w in ROMS.

This is a somewhat old page on that topic but I think it's the same now?

https://www.myroms.org/projects/src/ticket/486

-------------
C = Cu + Cv + Cw

where

Cu = ABS(u(i,j,k) + u(i+1,j,k)) * dt * pm(i,j)

Cv = ABS(v(i,j,k) + v(i,j+1,k)) * dt * pn(i,j)

Cw = ABS(wvel(i,j,k-1) + wvel(i,j,k)) * dt * Hz(i,j,k)
----------------

You can see the maximum Cu, Cv and Cw it in the log file and also the (i,j,k) location for said Cs:

------------
STEP Day HH:MM:SS KINETIC_ENRG POTEN_ENRG TOTAL_ENRG NET_VOLUME
C => (i,j,k) Cu Cv Cw Max Speed

960 40 00:00:00 8.657897E-04 1.948261E+04 1.948261E+04 2.182663E+17
(096,125,01) 9.919103E-03 4.299619E-03 1.211318E-02 1.049095E+00
-------------

nmichelet
Posts: 31
Joined: Fri Oct 02, 2015 2:24 pm
Location: Cerema

### Re: stability criterion

Thanks a lot this is very helpfull