Multiscale modelling of lubrication flows under rarefied gas conditions

We present a multiscale method for simulating non-equilibrium lubrication flows. The effect of low pressure or tiny lubricating geometries that gives rise to rarefied gas effects means that standard Navier–Stokes solutions are invalid, while the large lateral size of the systems that need to be investigated is computationally prohibitive for Boltzmann solutions, such as the direct simulation Monte Carlo method (DSMC). The multiscale method we propose is applicable to time-varying, low-speed, rarefied gas flows in quasi-3D geometries that are now becoming important in various applications, such as next-generation microprocessor chip manufacturing, aerospace, sealing technologies and MEMS devices. Our multiscale simulation method provides accurate solutions, with errors of less than 1% compared to the DSMC benchmark results when all modeling conditions are met. It also shows computational gains over DSMC that increase when the lateral size of the systems increases, reaching 2–3 orders of magnitude even for relatively small systems, making it an effective tool for simulation-based design.