Computing spherical surface integral for a Field in S2 basis

[Florian Schopper]

Hi everyone,

I have a Field in S2 coordinates/basis and want to integrate over the surface of the whole sphere, but can't seem to get it to work.

I saw in previous answers that using Average is a good workaround, but it also doesn't work on the S2 basis.

I then tried in BallBasis with r=1, but I still get an error:

coords = d3.SphericalCoordinates('theta', 'phi', 'r')

dist = d3.Distributor(coords, dtype=dtype)

ball = d3.BallBasis(coords, shape=(Nphi, Ntheta, Nr), radius=1, dealias=dealias, dtype=dtype)

sphere = ball.S2_basis()

n = dist.Field(name='n', bases=ball)

ct1 = dist.Field(name='ct1')

ct2 = dist.Field(name='ct2')

theta_grid, phi_grid  = dist.local_grids(sphere)

integral = lambda n: 4*np.pi * d3.Average(n, coords.S2coordsys)

problem = d3.IVP([n, ct1, ct2], namespace=locals())

problem.add_equation('dt(n(r=1)) = -D_CFG * (ct1 + ct2) + RE_AT * (N_CFG - integral(n(r=1)))')

this produces the error:

No subclasses of <class 'dedalus.core.operators.Convert'> found for the supplied arguments: (Mul(-1, Add(Convert(Mul(-0.0001, Add(<Field 140217378309408>, <Field 140217378309584>))), Mul(1e-06, Add(Convert(<Field 140217378310992>), Mul(-1, Mul(144.0, Mul(3.141592653589793, Mul(4.0, Mul(1.5546823183243522e+72, Average(interp(<Field 140217378309232>, r=1))))))))))), <dedalus.core.basis.SphereBasis object at 0x7f86ecf79eb0>), {}

If I change it to use integral(n) in the equation and d3.Average(n(r=1), coords.S2coordsys) above, it is the same error.

It only works if I remove the (r=1) but I don't want to compute the problem for the whole sphere.

Has anyone encountered this issue and found a solution?

Kind regards,

Florian

[Jeffrey S. Oishi]

Hi Florian,

This is not yet implemented. We will be implementing it soon.

Jeff

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