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

[Ulf Schiller]

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

smime.p7s
Description: S/MIME Cryptographic Signature