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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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