Fast continuity correction method for computation of incompressible fluid flows with free surface

A new effective numerical scheme for the treatment of excess mass is described here. The scheme was incorporated in the new numerical model, KU-2DVFF-03. The excess masses generated during the computation of the momentum equations should be pushed away from the grid point of interest to satisfy the continuity equation. The present method adopted "double-double sweep" procedure to relocate the excess masses in contrast to the previous even distribution in the 4 directions. The free surface was either vertical or horizontal in the existing models, e.g. NASA-VOF2D. The free surface is treated differently from previous methods. The slopes are assumed to be vertical, horizontal, or 45degrees-inclined in the new scheme. The water levels are defined on the horizontal center-line, vertical center-line, or 45degrees-inclined line which is the center-line of the 45degrees-inclined grid point.