A conservative level set method for two phase flow II

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 U 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 U goes smoothly from zero to one. The interface is moved implicitly by the advection of U, which is split into two steps. First U is advected using a standard numerical method. Then an intermediate step is performed to make sure that the smooth profile of U and the thickness of the transition layer is preserved. Both these steps are performed using conservative second order approximations and thus conserving U. In this way good conservation of the area bounded by the 0.5 contour of U 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. 2005 Elsevier Inc. All rights reserved.