SURFACE-ADAPTIVE FINITE-VOLUME METHOD FOR SOLVING FREE SURFACE FLOWS

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Abstract
A method is presented for solving the primitive-variable equations of motion for viscous, incompressible, free-surface flows. The computational mesh defines quadrilaterals that are used as the control volumes in a finite-volume method in which the mesh moves to adapt to the free surface. Dependent variables are co-located at the center of each volume. The strength of the present method results from the innovative way in which the control volume corners, which define the surface location, are moved by applying a „natural“ closure of the mass and momentum equations along the surface. This avoids the need for a separate kinematic condition while ensuing that the kinematic condition is exactly satisfied. The results of several test problems are provided, including sloshing in a tank, propagation of a solitary wave, and filling of tanks.

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