A wall-function viscosity model based on gas molecular dynamic simulation and its application

This paper introduces a first-order velocity slip model combined with a viscosity model that effectively captures the nonlinear velocity profile in the Couette flow problem within the slip flow regime. A wall-function model that accounts for rarefaction effects is derived for gas viscosity using the Direct Simulation Monte Carlo (DSMC) method. The new first-order velocity slip model is applied to the Navier–Stokes (N–S) equations. The proposed wall-function viscosity model considers the effect of flow rarefaction and is applicable to different types of gases. The velocity slip coefficient is validated by comparing the numerical results with those obtained via the DSMC method. There is good agreement between the velocity profiles obtained using the proposed slip model and those from the DSMC method. The nonlinear velocity profiles near the walls are well captured using the proposed first-order slip model. This study demonstrates that the accuracy of numerical simulations of rarefied gas flows via the N–S equations can be improved by incorporating viscosity models that consider rarefaction effects, allowing for the use of simpler velocity slip models instead of higher-order models.