[FLASH-USERS] Numerical Viscosity

[Dean Townsley]

Hi Markus,

Quantifying implicit numerical viscosity is a tricky business, since I 
think it can behave in unphysical ways.  That being said it, I think it 
is not too ill-defined to estimate a sort of "effective" implicit 
viscosity for the dissipation of turbulence in your simulation.  The 
"proper" way to do this is to measure the turbulence cascade in your own 
simulation and then infer the viscosity from the behavior of that at 
small scales.  This also demonstrates that you have something that would 
be thought of as turbulence in your simulation at all, which requires 
fairly good resolution.  An easier way is to use something estimated for 
a similar hydro method.  The reference that comes to mind is Aspden, 
Nikiforakis, Dalziel and Bell (2008, 
http://dx.doi.org/10.2140/camcos.2008.3.103).  They don't use the exact 
hydro method that is in flash, but they do explore some similar ones.

Quoting some results from that...
Note that things might not be as simple as you might think because the 
viscosity actually depends on the strength of your turbulence and how 
well the integral scale is resolved.  The effective viscosity they find is

   nu_e = epsilon^1/3 * 0.203*N^0.102 * deltax^4/3

Where epsilon is the dissipation rate and N is the number of 
computational cells across the integral length scale.  This puts the 
Kolmogorov scale generally between 1/5 and 1/3 of the cell size, 
depending on the details.

If you're more interested in viscosity in shear flows rather than 
turbulence, I believe physicality gets even more tricky.

Hopefully that's helpful.  If you're actually using the MHD solver, then 
I'll leave that to others to comment on.  (I didn't think the 
staggered-mesh characteristic was important for non-M HD, but others can 
correct me.)

Dean

On 02/05/2016 06:21 AM, Markus Haider wrote:
> Dear FLASH users,
>
> I am using FLASH for a galaxy cluster simulation, using the unsplit 
> staggered mesh solver. The resolution of our simulation is 14 kpc/h. I 
> was wondering how to characterize the influence of numerical viscosity 
> on our simulations. Is there a way to compute the viscosity?
>
> Best regards,
> Markus Haider
>
>