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A stable and accurate time-marching pressure-correction/Taylor-Galerkin finite element algorithm is presented to accommodate low Mach number compressible and incompressible viscoelastic liquid flows. The algorithm is based on an operator splitting constructive process that discloses three fractional stages. For the compressible regime, a piecewise-constant density interpolation with gradient recovery is employed, for which the background theory and consistency of approach are discussed. The scheme is applied to contraction flows for Oldroyd model fluids, covering entry-exit flows and high pressure-drop situations. Stability and performance characteristics of the new algorithmic implementation are highlighted. Solutions are provided for a range of compressible settings, tending to the incompressible limit at vanishing Mach number.

This numerical study focuses on regularised Bingham-type and viscoelastoplastic fluids, performing simulations for 4:1:4 contraction-expansion flow with a hybrid finite element-finite volume subcell scheme. The work explores the viscoplastic regime, via the Bingham-Papanastasiou model, and extends this into the viscoelastoplastic regime through the Papanastasiou-Oldroyd model. Our findings reveal the significant impact that elevation has in yield stress parameters, and in sharpening of the stress singularity from that of the Oldroyd/Newtonian models to the ideal Bingham form. Such aspects are covered in field response via vortex behaviour, pressure-drops, stress field structures and yielded-unyielded zones. With rising yield stress parameters, vortex trends reflect suppression in both upstream and downstream vortices. Viscoelastoplasticity, with its additional elasticity properties, tends to disturb upstream-downstream vortex symmetry balance, with knock-on effects according to solvent-fraction and level of elasticity. Yield fronts are traced with increasing yield stress influences, revealing locations where relatively unyielded material aggregates. Analysis of pressure drop data reveals significant increases in the viscoplastic Bingham-Papanastasiou case, O (12%) above the equivalent Newtonian fluid, that are reduced to 8% total contribution increase in the viscoelastoplastic Papanastasiou-Oldroyd case. This may be argued to be a consequence of strengthening in first normal stress effects.Peer reviewe