Three-dimensional transient free-surface flow of viscous fluids inside cavities of arbitrary shape

The three-dimensional transient free-surface flow inside cavities of arbitrary shape is examined in this study. An adaptive (Lagrangian) boundary-element approach is proposed for the general three-dimensional simulation of confined free-surface flow of viscous incompressible fluids. The 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 cubic, rectangular and cylindrical containers. These problems illustrate the transient nature of the flow during the mixing process. Surface tension effects are also explored.