[MITgcm-devel] viscosity on CS grid

[Alistair Adcroft]

Curious that we argued for Leith because we couldn't do Smagorinsky on 
the cube but then didn't test it on the cube before making some really 
great movies!

I think the over-computing and on-tile halo-halo copy solution is best 
and least intrusive. I had to deal with this in the grid-based viscosity 
code also (I think).

A.

Jean-Michel Campin wrote:
> Hi,
> 
> it seems to me that we have 2 problems with horizontal 
> viscosity on the cubed-sphere grid, at the corners:
> 
> 1) Leith scheme (C2 or C4):
> for example, SW corner:
> vort3(0,1) is not computed (set to zero).
> but is used to compute viscAh_D(0,1) and viscAh_Z(1,1)
> and later uDissisp(1,1).
> This means that we will get different values
> on the 2 faces for the same physical point on the edge 
> of the cube, near a corner.
> 
> 2) biharmonic viscosity:
> generally requires Olx=3,Oly=3.
> but around the corner, we have some problems to compute
> del2u,del2v on a wide enough stencil. At the end
> uDissisp & vDissisp are not correct (different values
> on the 2 faces for the same physical point on the edge 
> of the cube, near a corner).
> 
> I can see 2 type of solutions:
> a) add an exchange of del2u & del2v to fix the biharmonic
> problem. Unfortunately, del2u &  del2v are only 2D local
> arrays, inside bi,bj loop. It means that the need to split
> the bi,bj loops, may be also the k loop, a pain.
> To fix the Leith scheme, we need to exchange the vorticity (vort3),
> same problem with local array inside bi,bj loops, but in addition,
> we still don't have the routine to do the exchange at a corner
> of the C-grid.
> Apart from the modifications needed in the code, those additional
> exchanges will slow down the model.
> 
> b) try to fix the Leith scheme without additional exchange,
> by computing the relative vorticity over a wider stencil.
> I started to change EXCH_UV and it doesn't seem impossible
> to make it work (still few problems with grid length
> and grid cell area).
> Now, if this works, this will reduce the biharmonic problem
> to only the gradient of divergence part of the flow (since the 
> vorticity will be available where it's needed), and this can be 
> fixed without additional exchanges, like the multidimension advection
> (for each direction, do a local copy into the corner-halo region 
> from the same tile, before computing each gradient component).
> 
> Comments/suggestions ?
> 
> Jean-Michel
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-- 
Dr Alistair Adcroft            http://www.mit.edu/~adcroft
MIT Climate Modeling Initiative        tel: (617) 253-5938
EAPS 54-1624,  77 Massachusetts Ave,  Cambridge,  MA,  USA