Development of an optimal hybrid finite volume/element method for viscoelastic flows

A cell-vertex hybrid finite volume/element method is investigated that is implemented on triangles and applied to the numerical solution of Oldroyd model fluids in contraction flows. Particular attention is paid to establishing high-order accuracy, whilst retaining favourable stability properties. Elevated levels of elasticity are sought. The main impact of this study reveals that switching from quadratic to linear finite volume stress representation with discontinuous stress gradients, and incorporating local reduced quadrature at the re-entrant corner, provide enhance stability properties. Solution smoothness is achieved by adopting the non-conservative flux form with area integration, by appealing to quadratic recovered velocity-gradients, and through consistency considerations in the treatment of the time term in the constitutive equation. In this manner, high-order accuracy is maintained, stability is ensured, and the finer features of the flow are confirmed via mesh refinement. Lip vortices are observed for We>1, and a trailing-edge vortex is also apparent. Loss of evolution and solution asymptotic behaviour towards the reentrant corner are also discussed.