Pressure driven rarefied gas flow through a slit and an orifice

The flow of a monatomic gas through a slit and an orifice due to an arbitrarily large pressure difference is examined on the basis of the nonlinear Bhatnagar–Gross–Krook (BGK) model equation, subject to Maxwell diffuse boundary conditions. The governing kinetic equation is discretized by a second-order control volume scheme in the physical space and the discrete velocity method in the molecular velocity space. The nonlinear fully deterministic algorithm is optimized to reduce the computational effort by introducing memory usage optimization, grid refinement and parallelization in the molecular velocity space. Results for the flow rates and the macroscopic distributions of the flow field are presented in a wide range of the Knudsen number for several pressure ratios. The effect of the various geometric and physical parameters on the flow field is examined. Comparison with previously reported corresponding Direct Simulation Monte Carlo (DSMC) results indicates a very good agreement, which clearly demonstrates the accuracy of the kinetic algorithm and furthermore the reliability of the BGK model for simulating pressure driven flows.

► Pressure driven flow of a rarefied gas through a slit and an orifice is simulated.
► The flow is modeled by nonlinear BGK equation subject to Maxwell boundary conditions.
► The code is optimized by parallelization, efficient memory handling and multigrid acceleration.
► The flow rates and the macroscopic distributions are accurate in the whole range of the Knudsen number.
► The proposed kinetic algorithm remains equally efficient for large and small pressure differences.