We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. The 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. A specific analysis on the influence of different choices of the mixture viscosity is also carried out.

翻译：本文提出了一种基于人工可压缩公式的不可压缩两相流隐式间断Galerkin（DG）离散方法。采用保守水平集（CLS）方法结合重新初始化过程捕捉移动界面。Navier-Stokes方程及水平集方法的时间离散采用基于L稳定的TR-BDF2投影方法，并利用自适应网格细化（AMR）增强两相流体界面处的分辨率。通过若干经典算例验证了所提方法的有效性，同时分析了不同混合黏度选择对计算结果的影响。