Kinetic boundary conditions in the lattice Boltzmann method

Details Kinetic boundary conditions in the lattice Boltzmann method Kinetic boundary conditions in the lattice Boltzmann method

2002-06-20

arxiv.org/abs/nlin/0206033v1

Nonlinear Sciences

Cellular Automata and Lattice Gases

14 pages, 2 Figures, To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.66.026311

Derivation of the lattice Boltzmann method from the continuous kinetic theory [X. He and L. S. Luo, {\it Phys. Rev. E} {\bf 55}, R6333 (1997); X. Shan and X. He, {\it Phys. Rev. Lett.} {\bf 80}, 65 (1998)] is extended in order to obtain boundary conditions for the method. For the model of a diffusively reflecting moving solid wall, the boundary condition for the discrete set of velocities is derived, and the error of the discretization is estimated. Numerical results are presented which demonstrate convergence to the hydrodynamic limit. In particular, the Knudsen layer in the Kramers' problem is reproduced correctly for small Knudsen numbers.

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