SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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High order boundary conditions for Lattice Boltzmann Schemes

M.M. Tekitek, F. Dubois and P. Lallemand

Our communication will be divided into two parts. In the first part, we show that it is possible to get the macroscopic fluid equations of lattice Boltzmann schemes with an external force using Taylor expansion. In a second part of our contribution, we validate this general expansion by a detailed application to boundary conditions.

[1] A. Augier, F. Dubois and B. Graille, Rotational invariance of Lattice Boltzmann schemes, 9th ICMMES Conference, Taipei, July 2012, to appear.
[2] F. Dubois, P. Lallemand and MM. Tekitek, On a superconvergent lattice Boltzmann boundary scheme, Computers and Mathematics with Applications, p. 2141-2149, 2010.
[3] D. d'Humières, Generalized Lattice-Boltzmann Equations, in \it Rarefied Gas Dynamics: Theory and Simulations, vol. 159 of \it AIAA Progress in Aeronautics and Astronautics, p. 450-458, 1992.
[4] D. d'Humières and I. Ginzburg, Multi-reflection boundary conditions for lattice Boltzmann models, Physical Review E 68 066614, 2003.

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