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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.

76M28 Particle methods and lattice-gas methods
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