Numerical Computation of 3-D Free Surface Flows by N-S Solver and Detection of Sub-breaking

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Abstract

The Navier-Stokes equation is directly solved by the finite-difference method to simulate 3-dimensional viscous flow fields with free-surface around a Wigley model. The body-fitted coordinates, non-staggered mesh system and the third-order upstream differencings for the convection terms are used in the present method. The solution procedure is a time-marching calculation of the velocities, followed by a solution of the pressure field in which the pressure iterations are made to reach convergence. A closer examination of the numerical scheme such as grid schemes and computing domains are made.<BR>It is found that either a narrow domain or a coarse grid system suppresses the development of the free-surface elevation. The computational results around the bow agree well with the experimental results even though the Reynolds number is not the same, but the stern flow does not. This may be partially due to the difference in the Reynolds number.<BR>The criterion for the sub-breaking is applied to the computed results. It detects the appearance of sub-breaking waves in the course of computation. The results corresponds to the observed free-surface flows.

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