How to build coarse-grain transport models consistent from the kinetic to fluid regimes

TL;DR

This paper develops a consistent coarse-grain transport model bridging kinetic and fluid regimes, incorporating internal energy states, reactive collisions, and thermodynamic reversibility, validated through shock wave simulations in nitrogen.

Contribution

It introduces a novel approach to derive fluid models from kinetic equations with internal energy and chemical processes, ensuring thermodynamic consistency and reversibility.

Findings

The model accurately predicts shock wave properties in nitrogen.

Kinetic and fluid simulations show good agreement in macroscopic quantities.

Reversibility relations are crucial for model thermodynamic consistency.

Abstract

In this paper, we examine how to build coarse-grain transport models consistently from the kinetic to fluid regimes. The internal energy of the gas particles is described through a state-to-state approach. A kinetic equation allows us to study transport phenomena in phase space for a non-homogeneous gas mixture. Internal energy excitation is modeled using a binary collision operator, whereas the gas chemical processes rely on a reactive collision operator. We obtain an asymptotic fluid model by means of a Chapman-Enskog perturbative solution to the Boltzmann equation in the Maxwellian reaction regime. The macroscopic conservation equations of species mass, mixture momentum, and energy are given, as well as expressions of the transport properties. Reversibility relations for elementary processes are formulated in the coarse-grain model at the kinetic level and are enforced in the collision algorithm of the direct simulation Monte Carlo method used to solve the kinetic equation. Furthermore, respecting these reversibility relations is key to deriving a fluid model that is well-posed and compatible with the second law of thermodynamics. Consistency between the kinetic and fluid simulations is assessed for the simulation of a shock wave in a nitrogen gas using the uniform rovibrational collisional coarse-grain model. The kinetic and fluid simulations show consistency for the macroscopic properties and transport fluxes between both regimes.