Abstract
A computational method has been proposed for viscous incompressible flows accompanied by oscillating free surfaces. The free surface profiles are represented by general curvilinear coordinates generated at every computational time step. The internal grid points are located by solving elliptic partial differential equations on the basis of the Arbitrary Lagrangian-Eulerian formulation. The transformed Navier-Stokes equations are discretized on the collocated grid arrangement. The velocity-pressure correction is performed with C-HSMAC method, which is effective for free-surface flows on the present coordinates and grid system. The computational method was applied to small amplitude standing waves under the effect of gravity and surface tension forces. In addition, it was also applied to non-linear waves caused by a pressure pulse imposed on a free surface. As a result, it has been shown that the predicted results are in good agreement with the theory and that the fluid mass is preserved with sufficient accuracy with the C-HSMAC method.
