A nonequilibrium-direction-dependent rotational energy model for use in continuum and stochastic molecular simulation

A new rotational energy exchange model for direct simulation Monte Carlo (DSMC) and multi-temperature Navier-Stokes methods is presented. The DSMC model is based only on collision-quantities and reduces to a rotational collision number in the continuum limit, applicable for use with the Jeans relaxation equation. The model is formulated based on recent Molecular Dynamics (MD) simulations of rotational relaxation in nitrogen (Valentini et al, Phys. Fluids 24, 106101 (2012)) and accounts for the dependence of the relaxation rate on the direction to the equilibrium state. This enables a single parameterization of the model to accurately simulate rotational relaxation in both compressing and expanding flows, unlike the widely used Parker model. The DSMC model is simple to implement, numerically efficient, and accurately reproduces a range of pure MD solutions including isothermal relaxations, normal shock waves, and expansions. This demonstrates that the complexity of a state-resolved model is not required for translational-rotational relaxation. A general form for the energy distribution function that should be sampled for post-collision states (using the Borgnakke-Larsen approach) is presented. This general formulation ensures detailed balance and equipartition of energy at equilibrium for any collision-quantity based DSMC model and also explains the behavior of prior rotational models in the literature. The model formulation is also general to the inelastic collision selection procedure used, which is shown to be a crucial aspect in implementing a DSMC collision model. Finally, the increased accuracy of a collision-quantity based model com- pared to a cell-averaged model is demonstrated by comparing rotational energy distribution functions within a shock wave against a pure MD solution.