Development of practical numerical methods for free surface flow

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l) The spatial divergence of velocities obtained by ordinary image processing for the breaking wave process is investigated to clarify the extent to which the mass conservation law is valid. It was found that the mass conservation law is more difficult to satisfy near the bottom and the free surface. A velocity correcting method which satisfies the mass conservation law by using a mass-consistent model was thus proposed. Breaker types (which axe judged conventionally by external factors), bottom slope and incident wave condition, can be determined by the internal characteristics with or without existing complex rotational motions.2) The numerical method used the Boundary-Fitted Coordinate (BFC) method consisting of the Boundary-Fitted Coordinates and Numerical Grid Generation technique. The accuracy of the present method was examined by performing calculations for a plunging breaker on a uniform slope. A comparison of both the numerical method and the experimental results from LDV and image processing immediately before the breaker confirmed the validity of the numerical method.3) A computational technique for improving the accuracy of both recognizing the free surface and satisfying mass-conservation in The Volume of Fluid (VOF) method is presented. Furthermore, because the advective equation of density functions is used for tracking free surface advection, a computational scheme having less numerical diffusion must be considered. Investigations of numerical diffusion in conventional numerical schemes indicated that the Cubic Interpolated Pseudo-particle (CIP) method associated with the Digitizer method (tangential transformation of density functions) is less diffusive.