| Issue |
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
|
|
|---|---|---|
| Page(s) | 1989 - 2034 | |
| DOI | https://doi.org/10.1051/m2an/2024063 | |
| Published online | 21 October 2024 | |
Analysis and numerical simulation of a generalized compressible Cahn–Hilliard–Navier–Stokes model with friction effects
1
Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions (LJLL), 75005 Paris, France
2
Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé, 59000 Lille, France
* Corresponding author: charles.elbar@sorbonne-universite.fr
Received:
11
May
2023
Accepted:
30
July
2024
We propose a new generalized compressible diphasic Navier–Stokes Cahn–Hilliard model that we name G-NSCH. This new G-NSCH model takes into account important properties of diphasic compressible fluids such as possible non-matching densities and contrast in mechanical properties (viscosity, friction) between the two phases of the fluid. The model also comprises a term to account for possible exchange of mass between the two phases. Our G-NSCH system is derived rigorously and satisfies basic mechanics of fluids and thermodynamics of particles. Under some simplifying assumptions, we prove the existence of global weak solutions. We also propose a structure preserving numerical scheme based on the scalar auxiliary variable method to simulate our system and present some numerical simulations validating the properties of the numerical scheme and illustrating the solutions of the G-NSCH model.
Mathematics Subject Classification: 35B40 / 35B45 / 35G20 / 35Q35 / 35Q92 / 65M08
Key words: Cahn–Hilliard equation / Navier–Stokes equation / asymptotic analysis / mathematical modeling / numerical simulations / scalar auxiliary variable method
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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