A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes
Abstract
In this article, we extend the Boltzmann framework for polyatomic gases by introducing quasi-resonant kernels, which relax resonant interactions, for which kinetic and internal energies are separately conserved and lead to equilibrium states with two temperatures. We establish an H-theorem and analyze the quasi-resonant model's asymptotic behaviour, demonstrating a two-phase relaxation process: an initial convergence towards a two-temperature Maxwellian state followed by gradual relaxation of the two temperatures towards each other. Numerical simulations validate our theoretical predictions. The notion of quasi-resonance provides the first rigorous framework of a Boltzmann dynamics for which the distribution is at all times close to a multi-temperature Maxwellian, relaxing towards a one-temperature Maxwellian.
Fields of Study & Subjects
Gas Dynamics and Kinetic Theory
Lattice Boltzmann Simulation Studies
Statistical Mechanics and Entropy
Publication details
- Journal / source
- ESAIM Mathematical Modelling and Numerical Analysis
- Publisher
- EDP Sciences
- Volume
- 60
- Issue
- 2
- Pages
- 473–494
- Publication date
- 20 January 2026
- Language
- EN