N‐space collision model for rotation‐translation energy exchange in DSMC collisions

Abstract

SummaryA new discrete simulation Monte Carlo (DSMC) collision model for molecules possessing an integer number of classical degrees of freedom for molecular structure energy is proposed. The total molecular energy (translation plus molecular structure) is represented by a velocity in five‐dimensional space. Each collision is an elastic N‐sphere collision in N‐space, where N= 3, 4, or 5. For N=5, there is a maximum chance of exchange of energy between the two components of velocity, which represent the rotation energy and the three components that represent the translational velocity. For N=3, there is no change in the rotation energy of each molecule, and for N=4, there is an intermediate chance that rotation and translation energy will be exchanged. The exchange probability ϕ can be set to give the desired rotational relaxation rate. To achieve any realistic viscosity μ(T), the N‐space model must be coupled with a modified collision procedure known as ν‐DSMC. The new model is shown to match the results of molecular dynamics calculations for the internal structure of a Mach 7 shock, with a saving of about 20% in CPU time compared to standard DSMC using the standard Borgnakke‐Larsen exchange model.