Vorticity confinement support

[Xayah-Hina]

Hi~ I noticed that field.curl for 3D is not yet supported, would this function to be supported in future version? thx~

# file '_field_math.py', line 647
def curl(field: Field, at='corner'):
    """
    Computes the finite-difference curl of the give 2D `StaggeredGrid`.

    Args:
        field: `Field`
        at: Either `center` or `face`.
    """
    assert 'vector' in field.shape, f"curl requires a vector field but got {field}"
    assert field.spatial_rank in (2, 3), "curl is only defined in 2 and 3 spatial dimensions."
    if field.is_grid and field.is_staggered and field.spatial_rank == 2 and at == 'corner':
......
    elif field.is_grid and field.is_centered and field.spatial_rank == 2 and at == 'corner':
...... 
    raise NotImplementedError("Only 2D curl at corner currently supported")

[holl-]

Hi @Xayah-Hina Do you need this for staggered or centered grids, and sampled at the corners or centers?

[Xayah-Hina]

Hi @Xayah-Hina Do you need this for staggered or centered grids, and sampled at the corners or centers?

Yes for staggered grids(velocity field) and centered grids(force fields). I also want some useful field operations like Helmholtz Decomposition for 3D vector fields. Is that possible to implement? thx~

[holl-]

The Helmholz Decomposition is basically what fluid.make_incompressible() does to compute the divergence-free veloctiy field and pressure. I think I'll have time to implement the curl next week. The default would be sampling the curl at the cell corners. Is that compatible with your method?

[Xayah-Hina]

The Helmholz Decomposition is basically what fluid.make_incompressible() does to compute the divergence-free veloctiy field and pressure. I think I'll have time to implement the curl next week. The default would be sampling the curl at the cell corners. Is that compatible with your method?

That's it! thanks so much~