A 3D strongly coupled implicit discontinuous Galerkin level set-based method for modeling two-phase flows

This work focuses on the development of a strongly coupled discontinuous Galerkin scheme for the modeling of unsteady incompressible inertial two-phase flows using the level set method. The new approach uses a discontinuous Galerkin discretization for both the incompressible Navier–Stokes and the level set equations and the whole system is solved in time using an implicit time integration scheme. Mass and energy conservation properties of the method are demonstrated and analyzed with various 2D and 3D numerical tests including the two-phase Poiseuille flow, the Rayleigh–Taylor instability and a sloshing problem.