High Knudsen Number Thermal Flows with the D2Q13 Lattice Boltzmann Model

Abstract

Lattice Boltzmann models have been successfully utilized to simulate conditions in rarefied flows. To further improve the characterization of transition flow expected in nano-scale channels, we explore implementing two wall-distance functions based on the integral of probability distribution functions to a D2Q13 model. A series of tests are performed to determine model performance in capturing the flow characteristics of highly rarefied conditions. The resulting model is validated using numerical data. The results show that the modified model is capable of simulating rarefied flow conditions, extending to the high end of the transition regime, up to Kn ∼ 5, representing a significant improvement over existing models.

Acknowledgments

The authors would like to thank Dr. Michael Gallis from Sandia National Laboratories for kindly providing the DSMC data for the rarefied Fourier flow case. This work was partially supported by the JSC Academic Fellowship Program sponsored by NASA.