An adaptive boundary-element approach for 3D transient free surface cavity flow, as applied to polymer processing

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. Several flow problems are presented to illustrate the utility of the approach, particularly as encountered in polymer processing. These problems illustrate the transient nature of the flow in the extrusion through circular and square dies, the filling of circular and square disks as in conventional injection molding, and the flow during gas-assisted injection molding inside a duct, with relevance to the important problem of viscous fingering.