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In this paper, we consider mathematical modeling and numerical simulation ofnon-isothermal compressible multi-component diffuse-interface two-phase flowswith realistic equations of state. A general model with general referencevelocity is derived rigorously through thermodynamical laws and Onsager'sreciprocal principle, and it is capable of characterizing compressibility andpartial miscibility between multiple fluids. We prove a novel relation amongthe pressure, temperature and chemical potentials, which results in a newformulation of the momentum conservation equation indicating that the gradientsof chemical potentials and temperature become the primary driving force of thefluid motion except for the external forces. A key challenge in numericalsimulation is to develop entropy stable numerical schemes preserving the lawsof thermodynamics. Based on the convex-concave splitting of Helmholtz freeenergy density with respect to molar densities and temperature, we propose anentropy stable numerical method, which solves the total energy balance equationdirectly, and thus, naturally satisfies the first law of thermodynamics.Unconditional entropy stability (the second law of thermodynamics) of theproposed method is proved by estimating the variations of Helmholtz free energyand kinetic energy with time steps. Numerical results validate the proposedmethod.

Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state