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 [0,1] 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.

翻译：本文提出了两种新的数值格式，采用时间有限差分与空间有限元方法，用于逼近具有退化迁移率的Navier-Stokes-Cahn-Hilliard系统。所提出的格式具有守恒性、能量稳定性，并能近似保持最大值原理（相变量超出区间[0,1]的量值随截断参数趋于零）。此外，我们通过若干数值算例展示了所提格式的精度与良好性能，并与常迁移率Navier-Stokes-Cahn-Hilliard模型的行为进行了对比。