Stabilised computations for viscoelastic flows under compressible implementations

We analyse and contrast different stabilisation methodologies embedded within a time-marching incremental pressure-correction formulation. Numerical solutions are presented for an Oldroyd-B model under compressible implementations, considering flow through a planar four-to-one abrupt contraction. Various alternative stabilisation strategies and their combinations are analysed to hone the response of the base hybrid finite element/volume implementation. To reflect the stabilised properties of each scheme, the study interrogates levels of stable Weissenberg number (We) solution. Results indicate that most improvement has been encountered with a Strain-Rate Stabilisation scheme, where critical We-levels have more than doubled above neutral variants, while stress peaks levels have been constrained. Here, differed-correction characterises temporal error norm stress behaviour and the nature of the re-entrant corner stress singularity. At a selected We-level and under a specific flow setting, all scheme variants have produced similar salient-corner vortex behaviour, predicting vortex reduction under increasing We. In contrast, lip-vortex features are found to be significantly affected by the particular re-entrant corner treatment applied. When present, lip vortices grow with increasing We. Relaxation of the incompressible constraint points to important numerical anomalies, present under certain discretisations.