A New Mixed Finite-element for Calculating Viscoelastic Flow

Abstract A new mixed finite element has allowed us to calculate flows of Maxwell-B and Oldroyd-B fluids at very high values of the Deborah number, De . The element is divided into several bilinear sub-elements for the stresses, while streamline-upwinding is used for discretizing the constitutive equation. The method is applied to the stick-slip problem, the flow through a tapered contraction and the flow through four-to-one abrupt plane and circular contractions. Important corner vortices develop at high values of De in the circular contraction. We have not encountered upper limits for the Deborah number in our calculations with Oldroyd-B fluids.