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-ord er Galerkin finite elements with and without the Elastic-Viscous Split ting of the Stress (EVSS), as well as EVSS/Streamline-Upwind (SU), EVS S/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 ha ve been investigated. Among the schemes considered, only the hp-type, EVSS/SU and EVSS/SUPG finite element methods produce a stable and accu rate discretization for flow of viscoelastic fluids in smooth geometri es. 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 linea r convergence rate. Moreover, based on the global deviation from mass conservation it is found that the hp version of the finite element met hod is much more cost efficient (i.e., CPU savings of 75-90% per itera tion) than the lower-order methods considered. Finally, it is shown th at if the comparison between the lower- and higher-order schemes is ba sed on convergence of the stresses, the CPU saving would be even great er than that calculated based on mass conservation. This is due to the fact that when using lower-order techniques, the velocity field becom es relatively insensitive to element size at early stages of mesh refi nement while accurate determination of the stresses requires meshes wi th increasing refinement. This is particularly true when the SU method is used in flow geometries that exhibit steep stress boundary layers.