二维相场 Navier-Stokes Cahn-Hilliard 模型的简单、全离散、无条件能量稳定方法：涉及任意密度比

两相 Navier-Stokes Cahn-Hilliard (NSCH) 混合模型是模拟非匹配密度多相流的关键框架。 developing fully discrete, energy-stable schemes for this model remains challenging, due to the possible presence of negative densities. While various methods have been proposed, ensuring provable energy stability under phase-field modifications, like positive extensions of the density, remains an open problem. We propose a simple, fully discrete, energy-stable method for the NSCH mixture model that ensures stability with respect to the energy functional, where the density in the kinetic energy is positively extended. The method is based on an alternative but equivalent formulation using mass-averaged velocity and volume-fraction-based order parameters, simplifying implementation while preserving theoretical consistency. Numerical results demonstrate that the proposed scheme is robust, accurate, and stable for large density ratios, addressing key challenges in the discretization of NSCH models.