Communications in Mathematical Sciences

Volume 12 (2014)

Number 3

Two properties of two-velocity two-pressure models for two-phase flows

Pages: 593 – 600

(Fast Communication)



Frédéric Coquel (Ecole Polytechnique, Palaiseau, France)

Jean-Marc Hérard (EDF R&D, Chatou, France)

Khaled Saleh (EDF R&D, Chatou, France; UPMC Université Paris, France; CNRS, UMR, LJLL, Paris, France)

Nicolas Seguin (UPMC Université Paris, France; CNRS, UMR, LJLL, Paris, France; Inria Paris-Rocquencourt, le Chesnay, France)


We study a class of models of compressible two-phase flows. This class, which includes the Baer-Nunziato model, is based on the assumption that each phase is described by its own pressure, velocity, and temperature and on the use of void fractions obtained from an averaging process. These models are nonconservative and non-strictly hyperbolic. We prove that the mixture entropy is non-strictly convex and that the system admits a symmetric form.


two-phase flows, entropy, symmetrizable system

2010 Mathematics Subject Classification

35F55, 35L60, 76Txx

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