Finite element-discontinuous Galerkin method for the numerical simulation of two-phase flow

The subject of the lecture is the numerical simulation of two-phase flow of immiscible fluids. Their motion is described by the incompressible Navier-Stokes equations with piecewise constant density and viscosity. The interface between the fluids is defined with the aid of the level-set method using a transport first-order hyperbolic equation. The Navier-Stokes system equipped with initial and boundary conditions and transmission conditions on the interface between the fluids is discretized by the Taylor-Hood P2/P1 conforming finite elements in space and the second-order BDF method in time. The transport level-set problem is solved with the aid of the space-time discontinuous Galerkin method (DGM). The second part of the lecture is devoted to the theoretical analysis of the DGM for the level-set problem. Numerical experiments demonstrate the applicability, accuracy and robustness of the developed method.