On the edge-based smoothed finite element approximation of viscoelastic fluid flows

This article discusses the numerical simulation of viscoelastic fluid flows using the edge-based smoothed finite element method (ESFEM). The incompressible Navier-Stokes equations coupled with the Oldroyd-B constitutive relation are decoupled via the characteristic-based split scheme that enables the use of equal-order interpolation for the triple primitive variables. For this reason, the spatial discretization is implemented with linear three-node triangular elements which work very well with the ESFEM. Edge-based smoothing cells (SCs) are constructed on grounds of existing elements, directly underpinning the essential gradient smoothing procedure. New integration points are proposed within local SCs since the ESFEM enjoys the tremendous flexibility of the smoothed Galerkin weak-form integral. The discrete viscoelastic system is entirely formulated in the edge-based notion such that all gradient-related terms are readily smoothed cell-by-cell. Finally, several numerical examples are presented to demonstrate the desirable capability of the ESFEM.