We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. Conservative level set (CLS) method is employed in combination with a reinitialization procedure to capture the moving interface. A projection method based on the L-stable TR-BDF2 method is adopted for the time discretization of the Navier-Stokes equations and of the level set method. Adaptive Mesh Refinement (AMR) is employed to enhance the resolution in correspondence of the interface between the two fluids. The effectiveness of the proposed approach is shown in a number of classical benchmarks, such as the Rayleigh-Taylor instability and the rising bubble test case, for which a specific analysis on the influence of different choices of the mixture viscosity is carried out.

翻译：本文提出了一种基于人工压缩公式的不可压缩两相流隐式间断伽辽金（DG）离散格式。采用保守水平集（CLS）方法结合重新初始化过程来捕捉移动界面。采用基于L-稳定TR-BDF2方法的投影格式对Navier-Stokes方程和水平集方法进行时间离散。采用自适应网格细化（AMR）技术来增强两相流体界面处的分辨率。通过一系列经典基准算例，如Rayleigh-Taylor不稳定性问题和上升气泡测试案例，展示了所提方法的有效性，并对混合粘度不同选择的影响进行了具体分析。