Unified Approach for Variable Collision‐Frequency Models in Rarefied Gas Dynamics

Abstract

An analytical version of the discrete‐ordinates method is used to develop solutions for some problems of the rarefied gas dynamics, based on a variable collision‐frequency model (CLF model) of the linearized Boltzmann equation. As much as possible, the solution is developed following a unified procedure for all problems considered, and the computational algorithm is implemented for three specific cases: the classical BGK model (constant collision frequency), the Williams model (the collision frequency is proportional to the magnitude of the velocity), and the rigid‐sphere model. Finite‐channel and half‐space problems are treated. In particular, numerical results obtained for the Poiseuille flow problem, the thermal‐creep problem and the thermal‐slip problem, are presented.

Keywords:

• Rarefied gas dynamics
• kinetic equations
• variable collision frequency models
• discrete ordinates method

10. Acknowledgments

The authors would like to thank R. D. M. Garcia and C. E. Siewert for important suggestions and helpful discussions regarding this work. The work of L.B.B. is supported, in part, by CNPq of Brasil.