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## Re: [ESPResSo-users] Lattice Boltzmann and the discretized Oseen Tensor

 From: Ulf Schiller Subject: Re: [ESPResSo-users] Lattice Boltzmann and the discretized Oseen Tensor Date: Tue, 19 Nov 2013 22:45:28 +0100 User-agent: Mozilla/5.0 (X11; Linux i686; rv:24.0) Gecko/20100101 Thunderbird/24.1.0

On 11/19/2013 10:28 PM, Vincent Ustach wrote:

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)



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.

Best,
Ulf

--
Dr. Ulf D. Schiller                        Building 04.16, Room 3006
Institute of Complex Systems (ICS-2)       Phone:   +49 2461 61-6144
Forschungszentrum Jülich, Germany          Fax:     +49 2461 61-3180



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