[MITgcm-devel] viscosity on CS grid

[Chris Hill]

JM

 (b) is definitely what I prefer. If it can work. The only missing bits is
RAZ I think?

 Alistair?

Chris 

> -----Original Message-----
> From: mitgcm-devel-bounces at mitgcm.org 
> [mailto:mitgcm-devel-bounces at mitgcm.org] On Behalf Of 
> Jean-Michel Campin
> Sent: Friday, September 17, 2004 9:52 AM
> To: MITgcm-devel at mitgcm.org
> Subject: [MITgcm-devel] viscosity on CS grid
> 
> 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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