Viscoelastic flow around a confined cylinder using spectral/hp element methods

The benchmark problem of flow of a viscoelastic fluid around a confined cylinder is considered. The governing equations are discretised using spectral/hp element methods. These allow the spatial and temporal variations in the solution that are characteristic of viscoelastic flows, to be resolved accurately and efficiently. 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 computations are stabilized using the DEVSS-G/DG formulation of the problem. Excellent agreement with the literature is achieved for the drag coefficient in the case of an Oldroyd-B fluid. Causes for the breakdown in numerical convergence with mesh refinement beyond some critical value of the Weissenberg number are explored. The high resolution property of spectral/hp approximations has enabled an instability that develops in the shear layer on the cylinder and is convected downstream to be identified. The onset of this instability is shown to occur at the critical value of the Weissenberg number predicted by the theory of Dou and Phan-Thien [9]. The influence of the Reynolds number and, for the Giesekus model, the mobility parameter on the drag coefficient is also investigated and discussed.