Recovery and stress-splitting schemes for viscoelastic flows

Abstract Various recovery and stress-splitting schemes are investigated numerically for an Oldroyd-B model within the general framework of a time stepping fractional-staged finite element formulation, that of a Taylor-Galerkin/pressure-correction method with consistent streamline upwinding. Smooth and non-smooth planar flows are cited and both creeping and inertial conditions are considered. Problems addressed include flow through 4:1 contraction geometries, with rounded or sharp re-entrant corners and flow past a cylinder. Vortex behaviour and scheme performance is analysed. The recovery-based schemes are stability enhancing, being superior in higher De attenuation over conventional and EVSS alternatives. It is the recovery aspect and not the stress-splitting, that is the key element responsible for this improvement. Considerable care must be exercised with time-stepping schemes of the pressure-correction form to sustain accuracy and stability.

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