# Discrete Boltzmann method with Maxwell-type boundary condition for slip flow

## TL;DR

This paper develops a discrete Boltzmann model with Maxwell-type boundary conditions to accurately simulate slip flow in microchannels, capturing velocity slip and Knudsen layer effects across various conditions.

## Contribution

It introduces a Maxwell-type boundary condition with tangential momentum accommodation coefficient into the discrete Boltzmann model for slip flow simulation.

## Key findings

- Successfully describes velocity slip and Knudsen layer effects.
- Validates the model with Couette and Poiseuille flow simulations.
- Clarifies the relation between different Knudsen number definitions.

## 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.