courant

[fereshteh]

Dear
how can i become sure that computed Courant Number is a nice value for my model. in my model dt=80s and model grid sizes are as:
Minimum X-grid spacing, DXmin = 3.33514538E+00 km
Maximum X-grid spacing, DXmax = 3.98831267E+00 km
Minimum Y-grid spacing, DYmin = 3.33800882E+00 km
Maximum Y-grid spacing, DYmax = 3.98739982E+00 km
Minimum Z-grid spacing, DZmin = 1.01057987E-01 m
Maximum Z-grid spacing, DZmax = 1.83012378E+02 m
Maximum grid stiffness ratios: rx0 = 2.334384E-01 (Beckmann and Haidvogel)
rx1 = 2.465125E+00 (Haney)
computed Courant numbers are:
Minimum barotropic Courant Number = 7.91482742E-03
Maximum barotropic Courant Number = 9.61417822E-02
Maximum Coriolis Courant Number = 8.52012048E-03
model runs without problem but please give me help that how i can find that Courant number is in good range.

Cheers
fereshte

[kate]

Those numbers all look good, well under 1.0. If the model is running, it's time to look elsewhere for issues. Do the flows and other fields look sensible?

[jivica]

From my point of view it is waste of CPU time to have CFL 0.1, but should look at the dynamics and make a few tests to be sure how far with dt you can go.
I believe Kate once wrote that for Rutgers version CFL should be less than 0.85.
Quick and dirty way you can compute it by yourself, for barotropic gravity wave it is function of minimum grid size and max depth.
dt=0.85./sqrt(9.81*grid.h.*(grid.pm.^2+grid.pn.^2))

Or as in ROMS code using real velocities:
search for Courant definition i.e on linux: grep Courant ~/roms/src/ROMS/Nonlinear/*.F
then look at the

Nonlinear/diag.F

and you will see:

Code: Select all

              my_Cu=0.5_r8*ABS(u(i,j,k,nstp)+u(i+1,j,k,nstp))*          &
     &              dt(ng)*pm(i,j)
              my_Cv=0.5_r8*ABS(v(i,j,k,nstp)+v(i,j+1,k,nstp))*          &
     &              dt(ng)*pn(i,j)
              my_Cw=0.5_r8*ABS(wvel(i,j,k-1)+wvel(i,j,k))*              &
     &              dt(ng)/Hz(i,j,k)
              my_C=my_Cu+my_Cv+my_Cw

Which is like dirty way I wrote but instead gravity speed sqrt(g*h)you use real one from the model.

Cheers,
Ivica

[fereshteh]

Dear jivica

it is function of minimum grid size and max depth
dt=0.85./sqrt(9.81*grid.h.*(grid.pm.^2+grid.pn.^2))

do you mean
grid.h= hmax
grid.pm=dx or 1/dx
grid.pn=dy or 1/dy
in both states dx and dy minimum?
thanks