Two methods of surface tension treatment in free surface flow simulations

We describe our approach to treatment of surface tension in free surface flow simulations on adaptive octree-type grids. The approach is based on the semi-Lagrangian method for the transport and momentum equations and the pressure projection method to enforce the incompressibility constrain. The surface tension contributes to the Dirichlet boundary condition for the pressure equation at the projection step. The treatment of surface tension is based either on accurate finite difference calculation of the mean curvature or on a curvature estimation by the implicit solution of conservative mean curvature flow problem. The first method provides almost the second order accuracy in space for surface tension forces. The second method is characterized by greater stability and essentially larger time steps. Numerical experiments illustrate the main features of the methods.