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In this work, a general formulation, which is based on steady boundary layer problems for the Boltzmann equation, of a half-space problem is considered. The number of conditions on the indata at the interface needed to obtain well-posedness is investigated. The solutions will converge exponentially fast “far away” from the interface. For linearized kinetic half-space problems similar to the one of evaporation and condensation in kinetic theory, slowly varying modes might occur near regime transitions where the number of conditions needed to obtain well-posedness changes (corresponding to transition between evaporation and condensation, or subsonic and supersonic evaporation/condensation), preventing uniform exponential speed of convergence. However, those modes might be eliminated by imposing extra conditions on the indata at the interface. Flow velocities at the far end for which regime transitions occur are presented for Boltzmann equations: for monatomic and polyatomic single species and mixtures; as well as bosons and fermions.

We present an optimization procedure in high-order lattice Boltzmann models in order to fine-tune the method for micro-channel flows in the transition region. Both the first and second slip coefficients are tunable, and the hydrodynamic and Knudsen layer solutions can be tailored. Very good results are obtained in comparison with the continuous solution for hard sphere molecules. For the first time, we provide an accurate description of Poiseuille flow in the transition region.

In this study, microscale gaseous flows in the transitional regime have been investigated by lattice Boltzmann method (LBM). In the existing microflows LBM models, the Knudsen layer correction function has been introduced into the models. According to the kinetic theory rigorously, we choose a proper expression of correction function, and then determine its adjustable parameter. A substitute high-order boundary conditions treatment is adopted to capture the velocity slip, without any difficulties in computing the high-order velocity derivatives. The numerical results of two typical microflows show that: the present results agree with the analytical solutions better than the existing LBM simulations. Evident improvements can also be found, especially for finite Kn microflows.

The evaporation and condensation of a polyatomic vapor in contact with its condensed phase has received much less attention than the monatomic case. In this paper we investigate the structure of the Knudsen layer formed in the steady evaporation and condensation of a vapor whose molecules behave as rigid rotators. The vapor motion is obtained by the numerical solution of the Boltzmann equation by the Direct Simulation Monte Carlo (DSMC) method. The obtained results are also compared with the solutions of a simplified kinetic BGK-like model equation. The relationships between the problem parameters are determined in numerical form for evaporation and condensation flows. It is shown that the present results are in good agreement with previous moment method investigations of evaporation flows.