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Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows

Published online by Cambridge University Press:  08 February 2013

Jianping Meng
Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK
Yonghao Zhang
Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK
Nicolas G. Hadjiconstantinou
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Gregg A. Radtke
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Xiaowen Shan
Beijing Aeronautical Science & Technology Research Institute, Commercial Aircraft Corporation of China, Ltd, Beijing, 102211, China


A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar–Gross–Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small-Mach-number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately $0. 5$ . On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased.

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