BGK and Fokker Planck Models for thermally perfect gases

TL;DR

This paper introduces BGK and Fokker-Planck models tailored for thermally perfect gases, accounting for high-temperature energy variations, and demonstrates their conservation, entropy properties, and connection to Navier-Stokes equations.

Contribution

It develops and analyzes new kinetic models for thermally perfect gases, incorporating energy models for high-temperature flows, with proven conservation and entropy properties.

Findings

Models satisfy conservation laws.

Models adhere to the H-theorem.

Derived Navier-Stokes asymptotics for the models.

Abstract

We propose two models of the Boltzmann equation (BGK and Fokker-Planck models) for rarefied flows of thermally perfect gases. These models take into account various models of energy, which are required for high temperature flows, like for atmospheric re-entry problems. We prove that these models satisfy conservation and entropy properties (H-theorem), and we derive their corresponding compressible Navier-Stokes asymptotics.