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性公式的隐式间断伽辽金（DG）离散方法，用于求解不可压缩两相流问题。采用保守水平集（CLS）方法结合重构程序捕捉运动界面。针对Navier-Stokes方程和水平集方法的时间离散，采用了基于L-稳定TR-BDF2方法的投影格式。通过自适应网格加密（AMR）技术增强两相流体界面处的分辨率。多个经典基准测试验证了所提方法的有效性。文中还特别分析了不同混合黏度选择对计算结果的影响。