Lattice Boltzmann modelling Knudsen layer effect in non-equilibrium flows

Due to its intrinsically kinetic nature, lattice Boltzmann (LB) approach to simulating non-equilibrium gas flows has recently attracted significant research interest. Compared with other kinetic methods, it can offer a significantly smaller computational cost. To capture the nonlinear high-order rarefaction phenomena in gas flows, a geometry-dependent gas local mean free path has been proposed to be implemented in our “high-order” LB model. A series of tests on rarefaction effects and the Knudsen layer interference have been carried out and the simulation results demonstrate our LB model’s capability for highly non-equilibrium flows. Introduction. – Understanding fluid flows possessing substantial non-equilibrium effects poses a long-standing challenge to fundamental statistical physics as well as many other science and engineering disciplines [1]. With rapid development of micro/nano fabrication technology, gas flows in micro/nano-fluidic devices have found a broad range of applications. Flows in these miniaturised devices are often non-equilibrium, which can be characterised by the Knudsen number (Kn), defined as the ratio of the gas molecular mean free path λ to the device characteristic length L. The Knudsen layer is the local non-equilibrium region extending several mean free paths from the wall. The momentum and heat fluxes, which are of most interest to designers in microflow and nanoflow applications, usually transfer from the boundaries to the bulk flow through this Knudsen layer. Because flows in the Knudsen layer are not in local thermodynamic quasi-equilibrium, the linear constitutive relations for shear stress and heat flux, which are assumed in the Navier-Stokes (NS) equations, are no longer valid in the Knudsen layer [2]. Figure 1 shows the schematic diagram of the velocity structure in the Knudsen layer of a shear driven flow. Although the NS equations with macro slip boundary condition can accurately predict the flow field outside the Knudsen layer, they fail to capture the flow characteristics in the Knudsen layer [3]. To simulate highly non-equilibrium flows, whether a model can capture the Knudsen layer flow characters becomes essential because the Knudsen layer forms a large proportion of the flow domain. Traditionally, kinetic methods such as directly solving the Boltzmann equation or the direct simulation Monte Carlo (DSMC) method can offer accurate descrip(a)Electronic mail: [email protected] (b)Electronic mail: [email protected]