Extension of generic two-fluid VOF advection schemes to an arbitrary number of components

We propose a new and simple method to extend any two-fluid dimensionally split VOF schemes on Cartesian meshes to N-fluid problems in 2D and 3D. The method is symmetric by permutation of the fluids, so that it is independent of the ordering of materials and guarantees natural properties of the volume fractions. It relies on a new algorithm to post-process N independent calls to two-fluid numerical fluxes. Termination proof of the algorithm is given. Various numerical test cases for rigid body advection and rotation of three or four fluids in 2D are presented, along with a 3D example.