A new rotational energy exchange model for direct simulation Monte Carlo and multi-temperature Navier-Stokes methods is presented. The direct simulation Monte Carlo 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 simulations of rotational relaxation in nitrogen (Valentini et al., Physics of Fluids, Vol. 24, No. 10, 2012, p. 106101) 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 direct simulation Monte Carlo model is simple to implement, numerically efficient, and accurately reproduces a range of pure molecular dynamics solutions, including isothermal relaxations, normal shock waves, and expansions.Ageneral 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 direct simulation Monte Carlo 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 direct simulation Monte Carlo collision model. Finally, the increased accuracy of a collision-quantity-based model compared with a cell-averaged model is demonstrated by comparing rotational energy distribution functions within a shock wave against pure molecular dynamics solutions.
Bibliographical noteFunding Information:
This research is supported by NASA under grant NNX11AC19G. Zhang is also supported by the doctoral dissertation fellowship program at the University of Minnesota. Additional support is provided by the U.S. Air Force Office of Scientific Research (AFOSR) under grant FA9550-10-1-0075. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the AFOSR or the U.S. Government.