For decades, it has been observed that the commonly used Borgnakke–Larsen method for
energy redistribution in Direct Simulation Monte Carlo codes fails to satisfy the principle of
detailed balance when coupled to a wide variety of temperature dependent relaxation
models, while seemingly satisfying detailed balance when coupled to others. Many attempts
have been made to remedy the issue, yet much ambiguity remains, and no consensus
appears in the literature regarding the root cause of the intermittent compatibility of the …

It is often observed that Direct Simulation Monte Carlo (DSMC) simulations either fail or
succeed to reach and maintain equilibrium depending on the choice of temperature
dependent relaxation models for internal energy modes, with no clear consensus in the
literature as to why. This work alleviates the ambiguity regarding the root cause of these
failures by presenting a rigorous theoretical derivation of the requirement for satisfying
detailed balance within the Borgnakke-Larsen method for energy redistribution, which is …