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

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 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 as well as expressions of the transport properties are given. 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. The 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.