### Speaker

Dr
Hélène Mathis
(Université de Nantes)

### Description

We propose a model of liquid-vapor phase transition including metastable
states of the van der Waals Equation of State. The first part of the talk concerns
the thermodynamics model. Following the second principle, the problem boils
down to a minimization problem with constraints of the mixture energy. This
”static” description allows to recover the classical equilibria: pure liquid/vapor
states and a coexistence state (given by the Maxwell equal area rule). Then,
when assuming a dependency with respect to time, we define a dynamical sys-
tem with long time equilibria which are either the classical equilibria or the
metastable states. In a second part of the talk, we use the dynamical system
as a source term of a two-phase isothermal model. The homogeneous model
is hyperbolic under condition. However for smooth solutions, we manage to
prove that the regions of hyperbolically are invariant domains. We finish with
some numerical experiments, obtained by a finite volume scheme and a splitting
technique to handle the source term.