标题： 一种简单、全离散、无条件能量稳定的两相Navier-Stokes Cahn-Hilliard模型的任意密度比方法 显示英文标题

标题： A simple, fully-discrete, unconditionally energy-stable method for the two-phase Navier-Stokes Cahn-Hilliard model with arbitrary density ratios

摘要： 两相Navier-Stokes-Cahn-Hilliard（NSCH）混合物模型是模拟密度不匹配的多相流的关键框架。由于可能出现负密度，为该模型开发全离散且能量稳定的方案仍然具有挑战性。尽管已提出了多种方法，但在相场修正下确保可证明的能量稳定性，例如密度的正延拓，仍然是一个开放问题。 我们提出了一种简单、全离散且能量稳定的NSCH混合物模型方法，该方法确保了相对于能量泛函的稳定性，其中动能中的密度通过正延拓处理。该方法基于一种替代但等价的形式化表达，使用质量平均速度和基于体积分数的序参量，简化了实现过程同时保留了理论一致性。 数值结果显示，所提出的方案对于较大的密度比具有鲁棒性、准确性和稳定性，解决了NSCH模型离散化中的关键挑战。 显示英文摘要

摘要： The two-phase Navier-Stokes Cahn-Hilliard (NSCH) mixture model is a key framework for simulating multiphase flows with non-matching densities. 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.