Assessment of Translational Anisotropy in Rarefied Flows Using Kinetic Approaches (Preprint)

Several distinct modeling approaches are tested for their ability to resolve translational nonequilibrium phenomena that are common to but not unique to rarefied gas dynamic flowfields. The methods considered include DSMC, BGK, ES-BGK, Navier-Stokes, and an anisotropic model based on a first order expansion of the Boltzmann equation for a Maxwell gas possessing an anisotropic Maxwellian distribution function. For the large Mach number normal shock wave, ES-BGK shows fair-to-good agreement with DSMC, while numerical solution of the anisotropic model equations are rather poor. A semi-analytical solution for the anisotropic model compares rather well with DSMC results for the normal shock wave, suggesting that the equation set may indeed be quantitatively useful for modeling translational nonequilibrium. For the hypersonic sphere-cone flowfield, comparison of the directly sampled shear stress with the Navier-Stokes Chapman-Enskog and anisotropic value evaluated using the DSMC macroscopic properties shows that the anisotropic result offers qualitative improvement over the NS value over a broad range of rarefaction.