Bound preservation for the consistent and conservative phase-field method for compressible single-, two-, and N-phase flows

Bound-preserving analysis is performed for the consistent and conservative Phase-Field method for compressible N -phase flows ( N ⩾ 1 ). A convex admissible set is first proposed, which follows a physical energy constraint and only requires convex equations of state , independent of the multiphase flow models. Under piece-wise polynomial approximation and for the HLL flux, our analysis determines the requirements to preserve physical bounds. A new numerical Phase-Field flux vector is derived to maintain solutions in the admissible set. Our analysis consistently reduces to two- and single-phase flows and is general for any choice of phasic minimum pressures. A parabolic correction for conservation is proposed to develop a numerical approach that not only preserves physical bounds but also maintains consistency, conservation, and equilibria of velocity, pressure, and temperature. Various compressible single-/two-/ N -phase flows are investigated to verify the analysis and numerical approach. The extension of our analysis to general equations of state is also discussed and verified. • A physical energy constraint is derived, producing a model-independent admissible set for compressible N -phase flows. • Bound-preserving analysis is performed with piece-wise polynomial approximation and the HLL flux. • A new numerical Phase-Field flux vector is derived for bound preservation. • A parabolic correction is proposed for consistency, conservation, bound preservation, and equilibrium. • Extension to general equations of state is discussed.