  We propose a model that describes phase transition including meta\-stable
states present in the van der Waals Equation of State. From a convex
optimization problem on the Helmoltz free energy of a mixture, we deduce a
dynamical system that is able to depict the mass transfer between two phases,
for which equilibrium states are either metastable states, stable states or {a
coexistent state}. The dynamical system is then used as a relaxation source
term in an isothermal 4$\times$4 two-phase model. We use a Finite Volume scheme
that treats the convective part and the source term in a fractional step way.
Numerical results illustrate the ability of the model to capture phase
transition and metastable states.
