Numerical Analysis of Gas Flows in a Microchannel Using the Cascaded Lattice Boltzmann Method with Varying Bosanquet Parameter

Abstract. In this paper, a Cascaded Lattice Boltzmann Method with second order slip boundary conditions is developed to study gas flows in a microchannel in the slip and transition flow regimes with a wide range of Knudsen numbers. For the first time the effect of wall confinement is considered on the effective mean free path of the gas molecules using a function with nonconstant Bosanquet parameter instead of the constant one. The constant-force driven and pressure-driven gas flows in a long microchannel are simulated under different conditions. The results of the velocity profile, pressure distribution, and mass flow rate are in good agreement with the benchmark solutions and experimental data reported in the literature. The Knudsen minimum phenomenon is also well captured by the present model. The proposed Cascaded Lattice Boltzmann Method shows a clear improvement in predicting the flow behaviors of microchannel gas flows for the previous classic and Cascaded Lattice Boltzmann Method

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Keywords: Cascaded Lattice Boltzmann method ، Micro Poiseuille flows ، Boundary conditions ، Bosanquet parameter ، and Effective viscosity