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

An implicit DG solver for incompressible two-phase flows with an artificial compressibility formulation