Investigation of the ellipsoidal-statistical Bhatnagar–Gross–Krook kinetic model applied to gas-phase transport of heat and tangential momentum between parallel walls

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The ellipsoidal-statistical Bhatnagar–Gross–Krook (ES-BGK) kinetic model is investigated for steady gas-phase transport of heat, tangential momentum, and mass between parallel walls (i.e., Fourier, Couette, and Fickian flows). This investigation extends the original study of Cercignani and Tironi, who first applied the ES-BGK model to heat transport (i.e., Fourier flow) shortly after this model was proposed by Holway. The ES-BGK model is implemented in a molecular-gas-dynamics code so that results from this model can be compared directly to results from the full Boltzmann collision term, as computed by the same code with the direct simulation Monte Carlo (DSMC) algorithm of Bird. A gas of monatomic molecules is considered. These molecules collide in a pairwise fashion according to either the Maxwell or the hard-sphere interaction and reflect from the walls according to the Cercignani–Lampis–Lord model with unity accommodation coefficients. Simulations are performed at pressures from near-free-molecular to near-continuum. Unlike the BGK model, the ES-BGK model produces heat-flux and shear-stress values that both agree closely with the DSMC values at all pressures. However, for both interactions, the ES-BGK model produces molecular-velocity-distribution functions that are qualitatively similar to those determined for the Maxwell interaction from Chapman–Enskog theory for small wall temperature differences and moment-hierarchy theory for large wall temperature differences. Moreover, the ES-BGK model does not produce accurate values of the mass self-diffusion coefficient for either interaction. Nevertheless, given its reasonable accuracy for heat and tangential-momentum transport, its sound theoretical foundation (it obeys the H-theorem), and its available extension to polyatomic molecules, the ES-BGK model may be a useful method for simulating certain classes of single-species noncontinuum gas flows, as Cercignani suggested.