A Parallel Level-set Approach for Two-phase Flow Problems with Surface Tension in Three Space Dimensions

In this paper we present a parallel three-dimensional Navier–Stokes solver for incompressible two-phase flow problems with surface tension. It employs a standard finite difference 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 approach. 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 mollified signum function. 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. For the discretization of surface tension we need to apply a smoothing scheme near the free surface which leads to a first order convergence in the smoothing region. The parallelization of the code is based on conventional domain decomposition using MPI. We discuss the details of the method and present the results of several numerical experiments concerning mass conservation, convergence of curvature and convergence of the complete two-phase flow scheme. Furthermore, we give a comparison of our simulated results to physical data for the collapsing water column problem. Finally, we present the results of a direct numerical simulation of the dynamic contact angle behavior for a drop which moves down an inclined solid wall.