A comparative study of higher‐ and lower‐order finite element techniques for computation of viscoelastic flows

Abstract

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 cylinders 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., ...