Towards a monolithic multiphase flow solver via surface stress-based formulations

In this note we discuss the combination of the classical CSS and CSF approaches with special FEM techniques towards a fully implicit distance-free level set method. Based on a new surface stress formulation, neither normals nor curvature have to be explicitly calculated, and also the explicit redistancing can be avoided so that a monolithic formulation of the corresponding multiphase problem gets feasible. Prototypical numerical tests of benchmarking character for a rising 2D bubble are provided for validating the accuracy of this new approach.