Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions

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Abstract
The lattice Boltzmann method is developed to study gaseous slip flow in microchannels. An approach relating the Knudsen number with the relaxation time in the lattice Boltzmann evolution equation is proposed by using gas kinetic equation resulting from the Bhatnagar–Gross–Krook collision model. The slip velocity at the solid boundaries is obtained with kinetic theoryboundary conditions. The two-dimensional micro-Couette flow, micro-Poiseuille flow, and micro-lid-driven cavity flow are simulated using the present model. It is found that the numerical results agree well with available analytical and benchmark solutions.