
From:  Vincent Ustach 
Subject:  Re: [ESPResSousers] Lattice Boltzmann and the discretized Oseen Tensor 
Date:  Tue, 19 Nov 2013 22:33:03 0800 
On 11/19/2013 10:28 PM, Vincent Ustach wrote:>From the Oseen tensor it follows that u scales with F, \eta^{1} and r^{1}, so at a distance dx u~F/(/eta dx). Then g is just a unitless factor that depends on how u is averaged, for example, averaging over a spherical surface gives g=6\pi. For the LB lattice, g depends on the interpolation stencil and the exact location of the (singular) force relative to the lattice sites. In practice, one uses a value of g obtained from averaging over various locations within an elementary lattice cell. This is described in more detail in the review by Duenweg/Ladd in Adv. Poly. Sci. http://arxiv.org/abs/0803.2826.
Heres another theory question :)
Following Alrichs & Dunweg 1999 and Usta 2005, I have found the proper
offset for friction in Lattice Boltzmann. The one thing I do not
understand about the offset is how the Oseen Tensor becomes discretized to
u_av = F / (g eta dx)
Best,
Ulf

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