PRACTICAL EVALUATION OF 4 MIXED FINITE-ELEMENT METHODS FOR VISCOELASTIC FLOW

We apply four stress-velocity-pressure algorithms to calculate four be nchmark problems, i.e., the flow of a Maxwell fluid around a sphere, t hrough a wavy tube, through an abrupt contraction, and in circular ext rusion. For every flow, we use only one mesh, i.e., the same number of velocity nodes and the same boundary conditions for all algorithms. T he meshes are neither too coarse nor too refined in order to provide u s with a practical evaluation of the methods, i.e., a simple mixed met hod MIX0, the 4 X 4 element, and two types of interpolation for elasti c-viscous split stress (EVSS). We also investigate three methods of in tegration of the constitutive equations: Galerkin, SUPG, and SU. The p erformance of 4 X 4 and the high-order EVSS are about the same. It is shown that the performance of MIX0 can be remarkably stable and accura te with smooth problems or leads to very poor results in more difficul t cases. The low-order EVSS method is accurate, stable, and cheap in c omputer time. It should be a good candidate for three-dimensional deve lopments.