Many problems in science and engineering are characterized by the movement of free surfaces. The most familiar are those where the movement of the liquid–gas interface leads to waves. In fact, for most people the notion of fluid dynamics is immediately associated with the motion of waves. Waves in high sea states, waves breaking near shores and moving ships, the interaction of extreme waves with floating structures, the spillage of water on ships or offshore structures (so-called green water on deck) and sloshing are but a few examples of flows with free surface motion. Other applications include:

  • in industrial engineering: melts, stirring tanks, mould filling, extrusion, etc.;
  • in aerospace engineering: sloshing in the fuel tanks of satellites, water landings, etc.

The computation of free surface flows is difficult because neither the shape nor the position of the interface between gas and liquid is known a priori; on the contrary, it often involves unsteady fragmentation and merging processes. There are basically three approaches to the computation of flows with free surfaces:

  • interface fitting;
  • interface tracking; and
  • interface capturing methods.

In the interface fitting methods the free surface is treated as a boundary of the computational domain, where the kinematic and dynamic boundary conditions are applied. These methods cannot be used if the interface topology changes significantly, particularly if the problem leads to overturning or breaking ...

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