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A low‐dimensional spectral approach for transient free‐surface flow inside thin cavities of symmetric shape
Author(s) -
Zhang Sheng X.,
Khayat Roger E.
Publication year - 2002
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.347
Subject(s) - flow (mathematics) , laplace transform , mechanics , free surface , lubrication theory , transient (computer programming) , fourier transform , computation , geometry , mathematics , lubrication , mathematical analysis , physics , thermodynamics , computer science , algorithm , operating system
The lubrication theory is extended for transient free‐surface flow of a viscous fluid inside three‐dimensional cavities of general symmetric shape but of small thickness. The problem is closely related to the filling stage during the injection molding process. The moving domain is mapped onto a rectangular domain at each time step of the computation. A modified pressure is introduced, which in this case is governed by the Laplace's equation, and it is expanded in a Fourier series along the flow direction. The expansion coefficients are obtained using the finite‐difference method. This approach is valid for simple and complex cavities as illustrated for the cases of a flat plate and a curved plate. Only a few modes are needed to secure convergence in general. It is found that the flow behaviour is strongly influenced by the shape of the initial fluid domain, the shape of the cavity, cavity thickness, and the inlet flow. Copyright © 2002 John Wiley & Sons, Ltd.