[MITgcm-support] CFL condition for a Spherical Case

Benjamin Ocampo rurik at ualberta.ca
Wed Mar 9 17:33:44 EST 2016

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.

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