An Unsteady Single-phase Level Set Method for Viscous Free Surface Flows

The single-phase level set method for unsteady viscous free surface flows is presented. In contrast to the standard level set method for incompressible flows, the single-phase level set method is concerned with the solution of the flow field in the water (or the denser) phase only. Some of the advantages of such an approach are that the interface remains sharp, the computation is performed within a fluid with uniform properties and that only minor computations are needed in the air. The location of the interface is determined using a signed distance function, and appropriate interpolations at the fluid/fluid interface are used to enforce the jump conditions. A reinitialization procedure has been developed for non-orthogonal grids with large aspect ratios. A convective extension is used to obtain the velocities at previous time-steps for the grid points in air, which allows a good estimation of the total derivatives. In this report we discuss the details of such implementations. The method was applied to three unsteady tests: a plane progressive wave, sloshing in a two-dimensional tank, and the wave diffraction problem in a surface ship, and the results compared against analytical solutions or experimental data. The method can in principle be applied to any problem in which the standard level-set method works, as long as the stress on the second phase can be specified (or neglected) and no bubbles appear in the flow during the computation.