[MITgcm-devel] implicit diffusion of advection schemes

[Baylor Fox-Kemper]

> Chris, if I remember Baylor correctly, the centered scheme does  
> have some implicit diffusion, but it's just not systematic, whereas  
> the more sophisticated schemes direct the implicit diffusion  
> towards making the scheme stable, see here http:// 
> forge.csail.mit.edu/pipermail/mitgcm-support/2007-February/004605.html

The 2nd-order centered scheme does have errors that scale  
"diffusively"--as kappaimplicit4\nabla^4 T--only it's not guaranteed  
that kappaimplicit4 will even be positive.  The DST3 scheme and lax- 
wendroff fix things up to guarantee that the errors that scale as  
diffusivities are in fact diffusive (with positive diffusivity).

In fact, one way to consider the stabilization effect of adding  
hyperdiffusion to the point where kappaimplicit4+kappaexplicit4>0.   
This would be a necessary (but not sufficient) consequence of  
stabilizing all growing numerical instabilities.

Cheers,
   -Baylor

>
> Martin
>
> On 15 May 2007, at 21:30, chris hill wrote:
>
>> The centered scheme has no implicit diffusion, you out it in  
>> explicitly (otherwise its horribly dispersive i.e. grid noise  
>> everywhere). I told you this last week (and probably the week  
>> before).
>>
>> chris
>> Dimitris Menemenlis wrote:
>>> Jinlun, we have been using 3rd order direct space time with flux  
>>> limiter
>>> http://mitgcm.org/sealion/online_documents/node78.html
>>> for the cube runs.
>>> Advection schemes are a big black box for me.  Do you know if  
>>> central differencing is less diffusive than above scheme?
>>> Dimitris
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>>
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