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Assessment of the ellipsoidal-statistical Bhatnagar-Gross-Krook model for force-driven Poiseuille flows. (English) Zbl 1349.82058

Summary: We investigate the accuracy of the ellipsoidal-statistical Bhatnagar-Gross-Krook (ES-BGK) kinetic model for planar force-driven Poiseuille flows. Our numerical simulations are conducted using the deterministic discrete velocity method, for Knudsen numbers (\(Kn\)) ranging from 0.05 to 10. While we provide numerically accurate data, our aim is to assess the accuracy of the ES-BGK model for these flows. By comparing with data from the direct simulation Monte Carlo (DSMC) method and the Boltzmann equation, the ES-BGK model is found to be able to predict accurate velocity and temperature profiles in the slip flow regime \((0.01<Kn\leq 0.1)\), for both low-speed and high-speed flows. In the transition flow regime \((0.1<Kn\leq 10)\), however, the model does not quantitatively capture the viscous heating effect.

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
76N15 Gas dynamics (general theory)
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
65C05 Monte Carlo methods
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