SUMMARY
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.
This paper explores the application of the conservative integral form of the Navier-Stokes equations to interfacial (free surface) flow problems on standard staggered grids; derives analytical, therefore, accurate formulae to accurately calculate the mass and momentum fluxes on the faces of the u-control and v-control volumes on standard staggered grids; and develops the algorithm to calculate the control volume surface areas exposed to the water and the area exposed to the air.
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