Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

Abstract

The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been know that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model. Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model. To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified.

Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method

“…Specifically, has no influence for because of the conservation laws, and it enhances (reduces) the nonequilibrium effects for when is large (small). Moreover, for the DBM, it is convenient to have a proper kinetic boundary condition for capturing the velocity slip and flow characteristics in the Knudsen layer [ 45 ].…”

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“…The inherent advantages of the LBM, as one of the approximate solutions of the Boltzmann equation with a lower computational cost, cause the significant development of this method for simulating flows. Boltzmann's basic equations, LBM, have the power to simulate continuous and rarefied flows [9], [10], so further details of the thermodynamic imbalance behavior can be examined in this way [11], [12]. It is often used instead of the Navier-Stokes equation (NSE) because the solution of the Boltzmann equation (BE) is much simpler [13].…”

Specific heat ratio effects of compressible Rayleigh-Taylor instability studied by discrete Boltzmann method

“…And in the case of the NS failure, it is equivalent to a modified NS equations plus a coarse-grained model of TNE [25,29]. In recent ten years, DBM has been widely used in a variety of complex flow systems [30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],…”