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## [ESPResSo-users] LBM, speed of sound, stability

 From: Ivan Cimrak Subject: [ESPResSo-users] LBM, speed of sound, stability Date: Wed, 17 Dec 2014 13:12:45 +0100 User-agent: Mozilla/5.0 (Windows NT 6.3; WOW64; rv:24.0) Gecko/20100101 Thunderbird/24.6.0

Hi all,

In one of his emails Ulf Shiller explained that:

"you need to make sure that h*c_s^2/\nu is small to avoid nonlinear instabilities. h is the LB timestep, c_s is the speed of sound, and \nu is the kinematic viscosity. In the D3Q19 model, c_s^2=1/3*a^2/h^2, so a^2/(3*\nu*h) must be small. It may work with values O(1) but it is not
guaranteed."


Ulf, could you please give me the reason why this is necessary? And what does it mean "is small"? Are the values 0.1 - 0.99 ok?


Thanks,
Ivan

--
Ivan Cimrak
FRI Zilinska Univerzita v Ziline
personal web: http://www.kst.fri.uniza.sk/~icimrak/
cell-in-fluid group: http://cell-in-fluid.fri.uniza.sk