Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion

TL;DR

This paper derives a simplified multicomponent fluid model with heat conduction and mass diffusion from a more complex system using asymptotic analysis, ensuring mathematical consistency and convergence of solutions.

Contribution

It introduces a novel asymptotic derivation of a multicomponent compressible flow model with heat and mass transfer, linking hyperbolic and parabolic systems through entropy methods.

Findings

Derived the Type-I model as a high-friction limit of the Type-II model.

Established the entropy structure and hyperbolic-parabolic nature of the asymptotic model.

Proved convergence of solutions from the full system to simplified models.

Abstract

A Type-I model of a multicomponent system of fluids with non-constant temperature is derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The asymptotic model is shown to fit into the general theory of hyperbolic-parabolic systems, by exploiting the entropy structure inherited through the asymptotic procedure. Finally, by deriving the relative entropy identity for the Type-I model, two convergence results for smooth solutions are presented, from the system with mass-diffusion and heat conduction to the corresponding system without mass-diffusion but including heat conduction and to its hyperbolic counterpart.