An U‐ALE formulation of 3‐D unsteady viscoelastic flow

Abstract

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. Copyright © 1993 John Wiley & Sons, Ltd