Transient viscoelastic flows in planar contractions

This article considers transient flows for planar contractions and Oldroyd-B fluids, with increasing flow-rate boundary conditions. We employ a novel hybrid finite volume/element time-dependent algorithm. The hybrid scheme consists of a TaylorGalerkin finite element discretisation, and a cell-vertex fluctuation-distribution finite volume approach. These two approaches are coupled at each time-step to solve the parabolic/hyperbolic system of partial differential equations. The finite element section is applied to the mass and momentum conservation equations, whilst the hyperbolic constitutive equation is treated via finite volume discretisation. The application of this time-accurate scheme fluids reveals some novel features, in contrast to time-independent (constant flow-rate) driving boundary conditions. In particular, we highlight dynamic flow structure evolution on the field and in stress.