HIGHER ORDER GALERKIN TECHNIQUES IN VISCOELASTIC FLOWSIMULATION

A persistent problem in viscoelastic liquid flow simulation through a variety of flow ge ometries is the loss of convergence of numerical methods at high values of the characteristic Deborah number, which is the consequence of a change of type of the governing equations (i.e., from elliptic to hyperbolic). In this paper we demonstrate that, for this class of ellip- tic/hyperbolic problems, the p- and Ap-version of the finite element method provide a stable discretization. For Stokes flow problems, exponential convergence is obtained, while for lami nar Navier-Stokes problems, effective error indicators enable the use of an adaptive scheme to provide similar convergence. Viscoelastic fluid flow is considered for UCM and OLD-B fluids past a square arrangement of long, rigid, motionless cylinders, and are compared with exper-imental measurements, which show an excessive pressure drop attributed to elastic effects.