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Two properties of two-velocity two-pressure models for two-phase flows. (English) Zbl 1303.35069

Summary: We study a class of models of compressible two-phase flows. This class, which includes the Baer-Nunziato model [M. R. Baer and J. W. Nunziato, Int. J. Multiphase Flow 12, 861–889 (1986; Zbl 0609.76114)], 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
35F55 Initial value problems for systems of nonlinear first-order PDEs
35L60 First-order nonlinear hyperbolic equations
76T99 Multiphase and multicomponent flows

Citations:

Zbl 0609.76114
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