Three-dimensional transient free-surface rotating creeping flow

The three-dimensional transient free-surface flow inside cavities of arbitrary shape is examined in this study. AD adaptive (Lagrangian) boundary-element approach is proposed for the general three-dimensional simulation of free-surface flow of a viscous incompressible fluid originally partially filling the cavity. The flow is induced by the rotation of the bottom lid. The numerical method is stable as it includes remeshing capabilities of the deforming free surface, and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. The method is used to determine the flow field and free Surface evolution inside rectangular containers. These flow configurations illustrate the transient nature of the flow during the mixing process. Surface tension effects are also explored. (C) 2003 Published by Elsevier Ltd.