Volume 55, Number 4, July-August 2021
|Page(s)||1569 - 1598|
|Published online||29 July 2021|
A homogeneous relaxation low mach number model
Universitéde Toulon – IMATH, EA 2134, Avenue de l’Université, 83957 La Garde, France
2 MAP5 UMR CNRS 8145 – Université de Paris, 45 rue des Saints Pères, 75270 Paris Cedex 6, France
3 Inria – team ANGE and LJLL UMR CNRS 7598, 4 place Jussieu, 75005 Paris, France
Accepted: 30 June 2021
In the present paper, we investigate a new homogeneous relaxation model describing the behaviour of a two-phase fluid flow in a low Mach number regime, which can be obtained as a low Mach number approximation of the well-known HRM. For this specific model, we derive an equation of state to describe the thermodynamics of the two-phase fluid. We prove some theoretical properties satisfied by the solutions of the model, and provide a well-balanced scheme. To go further, we investigate the instantaneous relaxation regime, and prove the formal convergence of this model towards the low Mach number approximation of the well-known HEM. An asymptotic-preserving scheme is introduced to allow numerical simulations of the coupling between spatial regions with different relaxation characteristic times.
Mathematics Subject Classification: 35Q35 / 35Q79 / 65M25 / 76T10
Key words: Low Mach number flows / modelling of phase transition / relaxation model / HEM / HRM / analytical solutions / well-balanced scheme / asymptotic-preserving scheme
© The authors. Published by EDP Sciences, SMAI 2021
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