Re: [ESPResSo-users] Lattice Boltzman, order ~1 units

[Ulf Schiller]

Hi Vincent,

It depends on the units of course, but in principle I am not aware of 
such a limitation. Linear stability requires the eigenvalues of the 
collision operator to be in the range -1<\gamma<1, but this does in 
principle allow any value of the (dimensionless) viscosity between 0 and 
infinity. The domain where the lattice Boltzmann works reliably is much 
better characterized by dimensionless numbers, i.e., small Mach number 
and small Knudsen number. Note that the Knudsen number is proportional 
to the Mach number divided by the Reynolds number, so you can in 
principle have Kn->0 at constant Ma and Re->infinity (acoustic scaling). 
However, this will drive you to the edge of the stability region and 
typically requires a high grid resolution and small time step. The 
density can entirely be scaled out, since small Mach number corresponds 
to the incompressible limit (in fact, ESPResSo is, or was at some point, 
implemented that way to prevent round-off errors). Things become a bit 
more involved when fluctuations are included, as the unit of mass is 
typically scaled with the temperature, and too high a temperature may 
lead to negative LB populations. In this case, a slightly more stringent 
scaling h~a^{5/2} is required for convergence.

Hope this helps.

Best regards,
Ulf

On 06/29/2017 01:35 PM, Vincent Ustach wrote:
> Hi Espresso community,
>
> I have seen several mentions over the years in tutorials, emails, and 
> discussions that lattice Boltzmann works reliably only when density and 
> viscosity are order one. Is there a published reference that someone 
> would kindly send that illustrates these guidelines?
>
> Warm Regards,
>
> Vincent
>
> --Vincent Ustach
>    University of California, Davis

--
Dr. Ulf D. Schiller
Assistant Professor, Department of Materials Science and Engineering
Faculty Scholar, School of Health Research
Clemson University
161 Sirrine Hall
Clemson, SC 29634

Office: 299c Sirrine Hall
Phone: 1-864-656-2669
Fax: 1-864-656-5973

Any links in this email are rewritten by Proofpoint which is deployed by
Clemson CCIT. I have no control over this rewriting and do apologize for
the convoluted appearance.