[FLASH-USERS] Numerical Viscosity

[David Radice]

Hi Markus, Dean,

adding to this discussion. Not long ago I published a simple paper where we looked at numerical dissipation and bottleneck effect using the different solvers implemented in FLASH:

	http://comp-astrophys-cosmol.springeropen.com/articles/10.1186/s40668-015-0011-0

The context is core-collapse supernovae, but the results should be broadly applicable.

Best,
David

> On Feb 5, 2016, at 8:30 AM, Dean Townsley <Dean.M.Townsley at ua.edu> wrote:
> 
> 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
>> 
>> 
> 

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