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A Lagrangian boundary element approach to transient three‐dimensional free surface flow in thin cavities
Author(s) -
Zhang Jie,
Khayat Roger E.
Publication year - 2001
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.181
Subject(s) - free surface , mechanics , laplace's equation , flow (mathematics) , laplace transform , computation , boundary element method , plane (geometry) , domain (mathematical analysis) , finite element method , surface (topology) , geometry , boundary value problem , boundary (topology) , mathematics , classical mechanics , physics , mathematical analysis , thermodynamics , algorithm
The lubrication theory is extended for transient free‐surface flow of a viscous fluid inside a three‐dimensional thin cavity. The problem is closely related to the filling stage during the injection molding process. The pressure, which in this case is governed by the Laplace's equation, is determined using the boundary element method. A fully Lagrangian approach is implemented for the tracking of the evolving free surface. The domain of computation is the projection of the physical domain onto the ( x , y ) plane. This approach 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 © 2001 John Wiley & Sons, Ltd.