A COMPARATIVE-STUDY OF HIGHER-ORDER AND LOWER-ORDER FINITE-ELEMENT TECHNIQUES FOR COMPUTATION OF VISCOELASTIC FLOWS

The stability, accuracy, and cost efficiency of conventional lower-order Galerkin finite elements with and without the Elastic-Viscous Splitting of the Stress (EVSS), as well as EVSS/Streamline-Upwind (SU), EVSS/streamline-upwind Petrov-Galerkin (SUPG) and higher-order Galerkin (hp-type) finite elements for steady flow of an upper-convected Maxwell fluid past square arrays of cylinder and through a corrugated tube have been investigated. Among the schemes considered, only the hp-type, EVSS/SU and EVSS/SUPG finite element methods produce a stable and accurate discretization for flow of viscoelastic fluids in smooth geometries. Additionally, it has been demonstrated that the hp-finite element method gives rise to an exponential convergence rate toward the exact solution, while all the lower-order schemes considered exhibit a linear convergence rate. Moreover, based on the global deviation from mass conservation it is found that the hp version of the finite element method is much more cost efficient (i.e., CPU savings of 75-90% per iteration) than the lower-order methods considered. Finally, it is shown that if the comparison between the lower- and higher-order schemes is based on convergence of the stresses, the CPU saving would be even greater than that calculated based on mass conservation. This is due to the fact that when using lower-order techniques, the velocity field becomes relatively insensitive to element size at early stages of mesh refinement while accurate determination of the stresses requires meshes with increasing refinement. This is particularly true when the SU method is used in flow geometries that exhibit steep stress boundary layers.