Navier-stokes and burnett simulations of flows in microchannels

In recent years, there has been considerable interest in computing gas flows at high Knudsen numbers in microdevices. At low Knudsen numbers, models based on the solution of compressible Navier-Stokes equations with slip boundary conditions are adequate. At high Knudsen numbers, either higher-order (beyond Navier-Stokes) continuum equations or the particle methods such as Direct Simulation Monte Carlo (DSMC) are employed to compute the flows. Higher-order continuum approximations are based on the Chapman-Enskog expansion of Boltzmann equation (leading to Burnett and super-Burnett equations), or moment methods based on taking the moments of the Boltzmann equation with flow variables (leading to Grad's 13 moments equations or Levermore's moments equations for example). In this paper, history of the Burnett equations and a variety of Burnett approximations (conventional Burnett equations, augmented Burnett equations and BGK-Burnett equations) are discussed. The physical and numerical issues related to these approximations are discussed. Calculations are presented for both subsonic and supersonic flows in microchannels. These computations are compared with Navier-Stokes solutions with slip boundary conditions and DSMC solutions. The computations provide some assessment of Burnett equations for computing microchannel flows at high Knudsen numbers.