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Re: [ESPResSo-users] Lattice Boltzman, order ~1 units
From: |
Ulf Schiller |
Subject: |
Re: [ESPResSo-users] Lattice Boltzman, order ~1 units |
Date: |
Fri, 30 Jun 2017 09:02:24 -0400 |
User-agent: |
Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.1.0 |
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
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