A BGK model for high temperature rarefied gas flows

TL;DR

This paper introduces a BGK model tailored for high temperature rarefied gas flows, capable of incorporating complex energy modes and chemical reactions, enabling efficient and accurate simulations in regimes where traditional methods struggle.

Contribution

The paper presents a novel BGK model that aligns with arbitrary constitutive laws and is suitable for high temperature, rarefied gas flow simulations, bridging a gap in existing kinetic models.

Findings

The BGK model accurately captures non-equilibrium energy modes.

Numerical results agree with Navier-Stokes solutions in relevant regimes.

Computational cost is comparable to simple monoatomic gas models.

Abstract

High temperature gases, for instance in hypersonic reentry flows, show complex phenomena like excitation of rotational and vibrational energy modes, and even chemical reactions. For flows in the continuous regime, simulation codes use analytic or tabulated constitutive laws for pressure and temperature. In this paper, we propose a BGK model which is consistent with any arbitrary constitutive laws, and which is designed to make high temperature gas flow simulations in the rarefied regime. A Chapman-Enskog analysis gives the corresponding transport coefficients. Our approach is illustrated by a numerical comparison with a compressible Navier-Stokes solver with rotational and vibrational non equilibrium. The BGK approach gives a deterministic solver with a computational cost which is close to that of a simple monoatomic gas.