[MITgcm-support] advective fluxes and transports

[Baylor Fox-Kemper]

Small correction:
> P.S. Keep in mind that second-order centered is not totally without  
> 'diffusive' discretization errors, just that no effort is made to  
> exploit the diffusive errors to our advantage.  The discretization  
> errors in second order centered appear as a hyperdiffusion:  
> \nabla^4 T.  Fourth-order centered is less 'diffusive', with  
> discretization errors appearing only at \nabla^6 T.
This should say the 'diffusive' discretization errors in second order  
centered appear as a hyperdiffusion: \nabla^4 T.  Fourth-order  
centered is less 'diffusive', with 'diffusive' discretization errors  
appearing only at \nabla^6 T.

There are also dispersive advection errors appearing at \nabla^3 T   
and \nabla^5 levels respectively...

>
> Upwinding and flux-limiting exploit the fact that errors can be  
> steered toward monotonicity and stability by messing around with  
> diffusive errors at the cost of lower order accuracy. So, for  
> example, first order upwinding can be thought of as adding an  
> automatic \nabla^2 T diffusion to a second-ordered centered  
> scheme.  Third-order upwinding can be thought of as adding an  
> automatic \nabla^4 T hyperdiffusion to a fourth-order centered  
> scheme, etc.  But, the amount of diffusivity added is dependent on  
> velocity, e.g., the "effective kappa" added is proportional  
> gridscale*|U| in the first-order upwind versus second-order  
> centered.  Thus, it is hard to diagnose after the fact.  Comparing  
> ADVx and UTHMASS allows one to quickly do so.
>
> On Feb 13, 2007, at 2:44 PM, Dimitris Menemenlis wrote:
>
>> Baylor, for computation of transports, which diagnostic should one  
>> use: ADVx_TH, UTHMASS, or UVELTH?  To date I have been using  
>> UTHMASS but from your description below it sounds like it would be  
>> more accurate to use ADVx_TH ?  D.
>>
>>
>>> Hi Paola, UVELTH is just the correlation of the U and theta  
>>> fields, with
>>> temperature appropriate interpolated.  ADVx_TH is the advective  
>>> flux, which
>>> can include things like the variable grid box size with nonlinear  
>>> free
>>> surface, shaved cells, etc, as well as the flux-limiting  
>>> corrections.  UVELTH
>>> will be equivalent to ADVx_TH only with centered 2nd-order  
>>> advection and
>>> simple vertical discretization/boundary conditions. Cheers, -Baylor
>>
>>
>> -- 
>> Dimitris Menemenlis <menemenlis at jpl.nasa.gov>
>> Jet Propulsion Lab, California Institute of Technology
>> MS 300-323, 4800 Oak Grove Dr, Pasadena CA 91109-8099
>> tel: 818-354-1656;  fax: 818-393-6720
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>
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