A high resolution spectral element approximation of viscoelastic flows in axisymmetric geometries using a DEVSS-G/DG formulation

- DEVSS-G/DG formulation is used for viscoelastic flow past a sphere.
- Fine-scale features in the flow are resolved using spectral element approximations.
- Drag coefficients are presented for Oldroyd B and Giesekus models.
- The Giesekus model generates a reduction in drag compared to the Oldroyd B model for equivalent values of the Weissenberg number and viscosity ratio.
- Additional factors to the extensional properties of the model are shown to influence the critical value of the Weissenberg number.

The discretisation of benchmark viscoelastic flow problems in axisymmetric geometries using the spectral element method is considered. The computations are stabilized using the DEVSS-G/DG formulation of the governing equations. A decoupled approach is employed in which the conservation equations are solved for velocity and pressure and the constitutive equation (Oldroyd-B and Giesekus) are solved for the polymeric component of the extra-stress tensor. The method is validated for the start-up of transient Poiseuille flow for which an analytical solution exists. A comprehensive set of results is presented for flow past a fixed sphere for the Oldroyd B and Giesekus models. Excellent agreement is found with results in the literature on the drag experienced by the sphere. Evidence is provided which shows the existence of a limiting Weissenberg number due to the inability to resolve the high gradients in axial stress in the wake of the sphere through polynomial enrichment. The shear-thinning property of the Giesekus model leads to a reduction in drag compared to the Oldroyd B model at equivalent values of the Weissenberg number and viscosity ratio. The numerical simulations eventually fail to converge for the Giesekus model which suggests that factors other than solely extensional properties are responsible for this behaviour. The influence of the Reynolds number and, for the Giesekus model, the mobility parameter on the drag coefficient is also investigated and discussed.