Stabilised Finite Element Modelling of Oldroyd-B Viscoelastic Flows

T.J. Craven, J.M. Rees, and W.B. Zimmerman
University of Sheffield

The Oldroyd-B family of viscoelastic fluids are notoriously difficult to model numerically. Standard Galerkin finite element methods are prone to numerical oscillations, and solutions break down as fluid elasticity increases.

The situation can be remedied to a certain degree however through the addition of weak stabilisation terms to the Galerkin formulation.

We present a stabilised Galerkin/least squares implementation of the Oldroyd-B equations. The model is used to successfully compute two standard test problems in viscoelastic flows.