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An U‐ALE formulation of 3‐D unsteady viscoelastic flow
Author(s) -
Baaijems Frank P. T.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620360704
Subject(s) - viscoelasticity , mathematics , flow (mathematics) , galerkin method , euler's formula , objectivity (philosophy) , advection , mathematical analysis , calculus (dental) , physics , finite element method , geometry , engineering , structural engineering , medicine , philosophy , epistemology , dentistry , thermodynamics
The Arbitrary‐Lagrange‐Euler (ALE) formulation is applied to the analysis of unsteady viscoelastic flow of an Upper‐Convected‐Maxwell (UCM) medium. It is shown how the requirement of incremental objectivity affects the stress updating scheme. The current implementation of the ALE formulation uses the Time‐Discontinuous/Galerkin‐Least‐Squares (TD/GLS) method to handle the advective parts of the equations. Further, the ALE formulation is compared with an Updated‐ALE formulation that is shown to give comparable results but is much more cost effective. The technique presented is particularly effective for free surface flows. Three applications are given.