Hermitian finite elements for calculating viscoelastic flow

Abstract

Numerical calculations of the flow of viscoelastic fluids through an abrupt contraction are prone to important errors in the evaluation of the stress and velocity fields near the re-entrant corner. We introduce a new type of rectangular finite element for calculating viscoelastic flows. Hermitian shape functions are used for interpolating the velocity field, while the stress shape functions are able to represent every derivative of the velocity field. The domain of convergence in Deborah number for the flow of an Oldroyd-B fluid is extended by a factor of four by comparison with earlier calculations. The numerical results show important differences between plane and axisymmetric flows in a four-to-one abrupt contraction.