A Lagrangian boundary element approach to transient three-dimensional freesurface flow in thin cavities

The lubrication theory is extended for transient free-surface flow of a vis cous fluid inside a three-dimensional thin cavity. The problem is closely r elated to the filling stage during the injection molding process. The press ure, which in this case is governed by the Laplace's equation, is determine d using the boundary element method. A fully Lagrangian approach is impleme nted for the tracking of the evolving free surface. The domain of computati on is the projection of the physical domain onto the (x, y) plane. This app roach is valid for simple and complex cavities as illustrated for the cases of a flat plate and a curved plate. It is found that the flow behavior is strongly influenced by the shape of the initial fluid domain, the shape of the cavity, and inlet flow pressure. Copyright (C) 2001 John Wiley & Sons, Ltd.