A consistent and conservative phase-field method for compressible N-phase flows: Consistent limiter and multiphase reduction-consistent formulation

In the present study, a general numerical approach, consisting of a consistent limiter and the multiphase reduction -consistent formulation, is developed to solve the multiphase Euler/Phase-Field model for compressible N -phase (N 1) flows in a consistent and conservative fashion. The proposed method is general in the sense that it admits N different phases and is not restricted to a specific Phase -Field formulation. Not only is the volume fraction bounded and the mass nonnegative, the volume fractions also sum up to unity, preventing the production of fictitious phases, local voids, or overfilling. Velocity, pressure, and temperature equilibria are maintained across material interfaces. Various compressible N -phase problems including shocks and interfaces are performed to verify the analysis and demonstrate the efficacy of the method for N 2. Unphysical behavior in N -phase calculations (production of fictitious phases, local voids, and overfilling) due to inappropriate numerical treatment is discussed. Three variants for the Phase -Field mechanism are proposed, one of which is most efficient with increasing number of phases. Including the Phase -Field mechanism produces controllable interface thickness, thus effectively preventing numerical mixing of different phases due to numerical diffusion in shock -capturing schemes.