A conservative level set method for two phase flow

A conservative method of level set type for moving interfaces in divergence free velocity fields is presented. The interface is represented implicitly by the 0.5 level set of a function Φ being a smeared out Heaviside function, i.e., a function being zero on one side of the interface and one on the other. In a transition layer of finite, constant thickness Φ goes smoothly from zero to one. The interface is moved implicitly by the advection of Φ, which is split into two steps. First Φ is advected using a standard numerical method. Then an intermediate step is performed to make sure that the smooth profile of Φ and the thickness of the transition layer is preserved. Both these steps are performed using conservative second order approximations and thus conserving ∫Φ. In this way good conservation of the area bounded by the 0.5 contour of Φ is obtained. Numerical tests shows up to second order accuracy and very good conservation of the area bounded by the interface. The method was also coupled to a Navier–Stokes solver for incompressible two phase flow with surface tension. Results with and without topological changes are presented.