• interfacial (free surface) flow;
  • control volume method;
  • conservative integral form;
  • Navier–Stokes equations;
  • multiphase flow;
  • ocean surface wave


In this paper, a new numerical method is developed for two-dimensional interfacial (free surface) flows, based on the control volume method and conservative integral form of the Navier–Stokes equations with a standard staggered grid. The new method deploys two continuity equations, the continuity equation of the mass conservation for better convergence of the implicit scheme and the continuity equation of the volume conservation for the equation of pressure correction. The convection terms (the total momentum flux) on the surfaces of control volume are accurately calculated from the wet area exposed to the water, and the dry area exposed to the air. The numerical results produced by the new numerical method agree very well with the analytical solution, experimental images and experimentally measured velocity. Copyright © 2012 John Wiley & Sons, Ltd.