The direct simulation Monte Carlo (DSMC) method is used to solve the three-dimensional nano-scale gas film lubrication problem between a gas bearing slider and a rotating disk, and this solution is compared to the numerical solution of the compressible Reynolds equations with the slip flow correction based on the linearized Boltzmann equation as presented by Fukui and Kaneko [molecular gas film lubrication (MGL) method] [ASME J. Tribol. 110, 253 (1988)]. In the DSMC method, hundreds of thousands of simulated particles are used and their three velocity components and three spatial coordinates are calculated and recorded by using a hard-sphere collision model. Two-dimensional pressure profiles are obtained across the film thickness direction. The results obtained from the two methods agree well with each other for Knudsen numbers as large as 35 which corresponds to a minimum spacing of 2 nm. The result for contact slider is also obtained by the DSMC simulation and presented in this paper.
Alejandro Garcia, W. Huang, and D. B. Bogy. "Three-Dimensional Direct Simulation Monte Carlo Method for Slider Air Bearings" Physica of Fluids (1997): 1764. doi:http://dx.doi.org/10.1063/1.869293