In this paper, we present a new computational framework to approximate a Cahn-Hilliard-Navier-Stokes model with variable density and degenerate mobility that preserves the mass of the mixture, the pointwise bounds of the density and the decreasing energy. This numerical scheme is based on a finite element approximation for the Navier-Stokes fluid flow with discontinuous pressure and an upwind discontinuous Galerkin scheme for the Cahn-Hilliard part. Finally, several numerical experiments such as a convergence test and some well-known benchmark problems are conducted.

翻译：本文提出了一种新的计算框架，用于逼近具有可变密度与退化迁移率的Cahn-Hilliard-Navier-Stokes模型，该框架能保持混合物的总质量、密度的逐点有界性以及能量的递减性。该数值格式基于采用间断压力的有限元方法对Navier-Stokes流体流动进行近似，并采用迎风间断Galerkin格式处理Cahn-Hilliard部分。最后，进行了若干数值实验，包括收敛性测试以及一些经典的基准问题。