| Issue |
ESAIM: M2AN
Volume 57, Number 1, January-February 2023
|
|
|---|---|---|
| Page(s) | 69 - 106 | |
| DOI | https://doi.org/10.1051/m2an/2022065 | |
| Published online | 12 January 2023 | |
Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion
1
Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
2
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
* Corresponding author: stefanos.georgiadis@kaust.edu.sa
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.
Mathematics Subject Classification: 35Q35 / 76M45 / 76N15 / 76T30 / 80A17
Key words: Multicomponent systems / Euler flows / non-isothermal model / Chapman-Enskog expansion / hyperbolic-parabolic / relative entropy / Bott-Duffin inverse
© The authors. Published by EDP Sciences, SMAI 2023
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