  The following paper presents two simulation strategies for compressible
two-phase or multicomponent flows. One is a full non-equilibrium model in which
the pressure and velocity are driven towards the equilibrium at interfaces by
numerical relaxation processes, the second is a four-equation model that
assumes stiff mechanical and thermal equilibrium between phases or components.
In both approaches, the thermodynamic behaviour of each fluid is modelled
independently according to the stiffened-gas equations of state. The presented
methods are used to simulate the de-pressurization of a pipe containing pure
CO$_2$ liquid and vapour under the one-dimensional approximation.
