In this work we present two new numerical schemes to approximate the Navier-Stokes-Cahn-Hilliard system with degenerate mobility using finite differences in time and finite elements in space. The proposed schemes are conservative, energy-stable and preserve the maximum principle approximately (the amount of the phase variable being outside of the interval goes to zero in terms of a truncation parameter). Additionally, we present several numerical results to illustrate the accuracy and the well behavior of the proposed schemes, as well as a comparison with the behavior of the Navier-Stokes-Cahn-Hilliard model with constant mobility.

中文翻译：

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具有简并迁移率的 Navier-Stokes-Cahn-Hilliard 系统的结构保持有限元方案


在这项工作中，我们提出了两种新的数值方案，使用时间有限差和空间有限元来近似具有简并迁移率的 Navier-Stokes-Cahn-Hilliard 系统。所提出的方案是保守的、能量稳定的并且近似保留最大原理（在截断参数方面，在间隔之外的相位变量的量变为零）。此外，我们提出了几个数值结果来说明所提出方案的准确性和良好行为，以及与具有恒定流度的 Navier-Stokes-Cahn-Hilliard 模型的行为进行比较。