  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.
