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Capturing Knudsen layer phenomena using lattice Boltzmann model

Zhang, Yonghao and Gu, X.J. and Barber, Robert W. and Emerson, David (2006) Capturing Knudsen layer phenomena using lattice Boltzmann model. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 74 (4). ISSN 1063-651X

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Abstract

In recent years, lattice Boltzmann methods have been increasingly used to simulate rarefied gas flows in microscale and nanoscale devices. This is partly due to the fact that the method is computationally efficient, particularly when compared to solution techniques such as the direct simulation Monte Carlo approach. However, lattice Boltzmann models developed for rarefied gas flows have difficulty in capturing the nonlinear relationship between the shear stress and strain rate within the Knudsen layer. As a consequence, these models are equivalent to slip-flow solutions of the Navier-Stokes equations. In this paper, we propose an effective mean-free path to address the Knudsen layer effect, so that the capabilities of lattice Boltzmann methods can be extended beyond the slip-flow regime. The model has been applied to rarefied shear-driven and pressure-driven flows between parallel plates at Knudsen numbers between 0.01 and 1. Our results show that the proposed approach significantly improves the near-wall accuracy of the lattice Boltzmann method and provides a computationally economic solution technique over a wide range of Knudsen numbers.