The paper concerns the construction of a compressible liquid-vapor relaxation model which is able to capture the metastable states of the non isothermal van der Waals model as well as saturation states. Starting from the Gibbs formalism, we propose a dynamical system which complies with the second law of thermodynamics. Numerical simulations illustrate the expected behaviour of metastable states: an initial metastable condition submitted to a certain perturbation may stay in the metastable state or reaches a saturation state. The dynamical system is then coupled to the dynamics of the compressible fluid using an Euler set of equations supplemented by convection equations on the fractions of volume, mass and energy of one of the phases.
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Figure 1.
Isothermal curves of the van der Waals EoS in the
Figure 2.
Isothermal curves of the van der Waals EoS in the
Figure 9.
Metastable zone: vector field of the dynamical system (53) (light blue arrows). The red line corresponds to the line
Figure 3.
Spinodal zone: vector field of the dynamical system (53) (light blue arrows). The red line corresponds to the line
Figure 4.
Spinodal zone, from top to bottom. Trajectories of the dynamical system (53) in the
Figure 5.
Spinodal zone, from top to bottom. Trajectories of the dynamical system (53) in the
Figure 6.
Stable phase zone: vector field of the dynamical system (53) (light blue arrows). The red line corresponds to the line
Figure 7.
Stable phase zone. Trajectories of the dynamical system (53) in the
Figure 8.
Stable phase zone, from top to bottom. Trajectories of the dynamical system (53) in the
Figure 10.
Metastable state and perturbation within the phase. Top figure: trajectories of the dynamical system (53) in the
Figure 11.
Metastable state and perturbation within the phase. Top figure: trajectories of the dynamical system (53) in the
Figure 12.
Metastable state and perturbation outside the phase. From top to bottom: trajectories of the dynamical system (53) in the
Figure 13.
Metastable state and perturbation outside the phase. From top to bottom: trajectories of the dynamical system (53) in the
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