Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions

Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin’s projection approach. The free surface between the two fluid phases is tracked with a level set technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and third order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the level set function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface which leads to a first order convergence in the smoothing region.