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. (c) 2005 Elsevier B.V. All rights reserved.