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In this paper, we consider the capabilities of the Boltzmann equation withthe Shakhov and ellipsoidal models for the collision term to capture thecharacteristics of rarefied gas flows. The benchmark is performed by comparingthe results obtained using these kinetic model equations with direct simulationMonte Carlo (DSMC) results for particles interacting via ab initio potentials.The analysis is restricted to channel flows between parallel plates and weconsider three flow problems, namely: the heat transfer between stationaryplates, the Couette flow and the heat transfer under shear. The simulations areperformed in the non-linear regime for the 3He, 4He, and Ne gases. Thereference temperature ranges between 1 K and 3000 K for 3He and 4He and between20 K and 5000 K for Ne. While good agreement is seen up to the transitionregime for the direct phenomena (shear stress, heat flux driven by temperaturegradient), the relative errors in the cross phenomena (heat flux perpendicularto the temperature gradient) exceed 10% even in the slip-flow regime. Thekinetic model equations are solved using the finite difference latticeBoltzmann algorithm based on half-range Gauss-Hermite quadratures with thethird order upwind method used for the implementation of the advection.

Comparison of the Shakhov and ellipsoidal models for the Boltzmann equation and DSMC for ab initio-based particle interactions