[MITgcm-support] CFL condition for a Spherical Case

[Benjamin Ocampo]

Hi Martin:

Thank you very much. I will look into the parameters viscAhgrid and keep in
mind the CFL constraints as you have mentioned.

Cheers,
Benjamin

On Thu, Mar 10, 2016 at 9:41 AM, Martin Losch <Martin.Losch at awi.de> wrote:

> Benjamin,
>
> the most important constraint is the CFL number u*dt/dx < 1 (or 1/2) for
> stable explicit schemes. For that you need indeed the expected current
> velocity u, but since your are probably simulating an ocean system without
> surface gravity waves, you can probably estimate how large u will be, e.g.
> 1m/s is already quite fast. For a spherical (latlon) grid, you need use the
> smallest grid cell, i.e. the one closes to the poles, because dx =
> R*delta(phi)*cos(theta) for these grids. And then you have to test and find
> out how large your time step can be before the model explodes due the
> violation of the CFL criterion. The monitor output contains number that
> help in the process (advcfl_uvel_max, etc.), so it’s a good idea to have
> monitor output very often (even each timestep) in this testing phase.
>
> At low resolution, it is usually possible to choose an A_h that is small
> enough to not violate the criteria that you mentioned, but at the same time
> high enough to make the grid resolve the flow (and make it stable). The
> criteria for A_h can be difficult at high resolution; in that case I
> recommend the scaled parameters viscAhgrid, which need to be below 1 (to
> satisfy the stability criterion). They are then scaled by the grid step and
> the time step; see mom_calc_visc.F for more details, or the documentation <
> http://mitgcm.org/public/r2_manual/latest/online_documents/node86.htm>
>
> Martin
>
> > On 09 Mar 2016, at 23:33, Benjamin Ocampo <rurik at ualberta.ca> wrote:
> >
> > Hi All:
> >
> > I have some questions about setting the resolution of the runs in a
> spherical polar case:
> >
> > For the latitude (phi) and longitude (theta) coordinate system, there is
> a constraint (CFL) for how small I can make the grid-size for both phi and
> theta defined below where delta(phi) denotes the grid-size of phi:
> >
> >    A_h < (R^2 delta(theta)^2)/(2 delta(t))
> >
> >    A_h < (R^2 delta(phi)^2)/(2 delta(t))
> >
> > where R is the radius of the planet.
> >
> > 1) Is there another condition I can use that provides a maximum to the
> size of both delta(theta) and delta(phi)?
> >
> > The one I have read up on is the Reynold's number method but that
> assumes that I know the horizontal velocity scale beforehand.
> >
> > I want to determine how low I can make the resolution in my spherical
> polar runs such that the model will resolve at minimum computation cost.
> >
> > Cheers,
> > Benjamin
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>
>
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