The Cahn-Hilliard-Navier-Stokes (CHNS) system utilizes a diffusive phase-field for interface tracking of multi-phase fluid flows. Recently structure preserving methods for CHNS have moved into focus to construct numerical schemes that, for example, are mass conservative or obey initial bounds of the phase-field variable. In this work decoupled implicit-explicit formulations based on the Discontinuous Galerkin (DG) methodology are considered and compared to existing schemes from the literature. For the fluid flow a standard continuous Galerkin approach is applied. An adaptive conforming grid is utilized to further draw computational focus on the interface regions, while coarser meshes are utilized around pure phases. All presented methods are compared against each other in terms of bound preservation, mass conservation, and energy dissipation for different examples found in the literature, including a classical rising droplet problem.

翻译：Cahn-Hilliard-Navier-Stokes (CHNS) 系统采用扩散相场方法进行多相流体流动的界面追踪。近年来，针对CHNS的结构保持方法受到关注，旨在构建例如满足质量守恒或保持相场变量初始有界性的数值格式。本研究基于间断伽辽金方法，考虑并比较了文献中现有的解耦隐式-显式格式。对于流体流动，则采用标准的连续伽辽金方法。通过使用自适应共形网格，将计算重点进一步集中于界面区域，而在纯相区域则采用较粗的网格。针对文献中的不同算例（包括经典的液滴上升问题），本文对所有提出的方法在界保持性、质量守恒性和能量耗散性方面进行了比较分析。