On the modelling of polyatomic molecules in kinetic theory

TL;DR

This paper provides a comprehensive overview of three different approaches for modeling polyatomic molecules in kinetic theory, serving as a pedagogical guide and a practical reference for researchers.

Contribution

It introduces and compares three modeling approaches—internal states, energy levels, and energy quantiles—for polyatomic molecules in kinetic theory, highlighting their applications and advantages.

Findings

Detailed explanation of three modeling approaches

Comparison of approaches for different research needs

Practical guidance for numerical simulations like DSMC

Abstract

This communication is both a pedagogical note for understanding polyatomic modelling in kinetic theory and a ''cheat sheet'' for a series of corresponding concepts and formulas. We explain, detail and relate three possible approaches for modelling the polyatomic internal structure, that are: the internal states approach, well suited for physical modelling and general proofs, the internal energy levels approach, useful for analytic studies and corresponding to the common models of the literature, and the internal energy quantiles approach, less known while being a powerful tool for particle-based numerical simulations such as Direct Simulation Monte-Carlo (DSMC). This note may in particular be useful in the study of non-polytropic gases.