| Issue |
Math. Model. Nat. Phenom.
Volume 21, 2026
|
|
|---|---|---|
| Article Number | 1 | |
| Number of page(s) | 34 | |
| Section | Mathematical methods | |
| DOI | https://doi.org/10.1051/mmnp/2025031 | |
| Published online | 03 February 2026 | |
A conservative two-phase flow model with a nonlinear degenerate diffusion
1
Université de Toulon – IMATH,
EA 2134, 83957
La Garde,
France
2
Université Paris Cité, CNRS, MAP5,
F-75006
Paris,
France
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
4
April
2025
Accepted:
15
November
2025
This paper is motivated by the need to model the dynamics of liquid–vapor flows involving phase transitions in heat exchangers. In the low Mach number asymptotic limit, we derive a system of 1D conservation laws with heat transfers causing phase change, with a degenerate and nonlinear thermal diffusion coefficient. This degeneracy induces discontinuities on the solution, both on the enthalpy and the velocity. We provide explicit steady and travelling wave solutions, and derive suitable numerical schemes able to capture the moving discontinuities.
Mathematics Subject Classification: 35Q35 / 35Q79 / 65M25 / 76T10
Key words: Liquid–vapor phase transition / generalized Stefan problem / nonlinear degenerate diffusion / numerical schemes / discontinuity propagation
© The authors. Published by EDP Sciences, 2026
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