Discontinuous Galerkin Method for Incompressible Two-Phase Flows

In this contribution we present a local discontinuous Galerkin (LDG) pressure-correction scheme for the incompressible Navier–Stokes equations. The scheme does not need penalty parameters and satisfies the discrete continuity equation exactly. The scheme is especially suitable for two-phase flow when used with a piecewise-linear interface construction (PLIC) volume-of-fluid (VoF) method and cut-cell quadratures.