A subspace projection method for the implementation of interface conditions in a single-drop flow problem

We present a mesh moving method within a finite element context, where the interface conditions of a two-phase flow problem are conveniently included in suitable chosen subspaces of the general trial and testfunction spaces. A weak formulation of the two-phase flow problem including species transport is derived, where the problem specific function spaces are replaced by appropriate projections operating on standard function spaces. The transfer of the variational formulation to a finite element method is straightforward and results in one set of equations for both fluidic phases. This subspace projection method is applicable to a wide range of interfacial conditions for multiphase flow problems. The method is validated for single-drop flow problems including species transfer. Furthermore, an application to the simulation of stagnant caps is presented.