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Boundary conditions for the upwind finite difference lattice Boltzmann model: Evidence of slip velocity in micro-channel flow. (English) Zbl 1213.76150
Summary: We conduct a systematic study of the effect of various boundary conditions (bounce back and three versions of diffuse reflection) for the two-dimensional first-order upwind finite difference lattice Boltzmann model. Simulation of Couette flow in a micro-channel using the diffuse reflection boundary condition reveals the existence of a slip velocity that depends on the Knudsen number $$\varepsilon = \lambda/L$$, where $$\lambda$$ is the mean free path and $$L$$ is the channel width. For walls moving in opposite directions with speeds $$\pm u_w$$, the slip velocity satisfies $$u_{\text{slip}} = 2\varepsilon u_{\text{wall}}/(1 + 2\varepsilon)$$. In the case of Poiseuille flow in a micro-channel, the slip velocity is found to depend on the lattice spacing $$\delta s$$ and Knudsen number $$\varepsilon$$ to both first and second order. The best results are obtained for diffuse reflection boundary conditions that allow thermal mixing at a wall located at half lattice spacing outside the boundary nodes.

##### MSC:
 76M28 Particle methods and lattice-gas methods
##### Keywords:
Lattice Boltzmann; Boundary conditions; Slip velocity
HE-E1GODF
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