Simulation for viscoelastic flow by a finite volume/element method Original Research Article

Stability of a second-order finite element/finite volume (FE/FV) hybrid scheme is investigated on the basis of flows with increasing Weissenberg number. FEs are used to discretise the balances of mass and momentum. For the stress equation a FV method is used, based on the recent development with fluctuation distribution schemes for pure convection problems. Examples considered include a start-up channel flow, flow past a cylinder and the non-smooth 4:1 contraction flow for an Oldroyd-B fluid. A considerable gain in efficiency per time step can be obtained compared to an alternative pure FE implementation. A distribution based on the flux terms is unstable for higher Weissenberg numbers, and this is also true for a distribution based on source terms alone. The instability is identified as being caused by the interaction of the balance equations and stress equation. A combination of distribution schemes based on flux and source terms, however, gives a considerable improvement to the hybrid FE/FV implementation. With respect to limiting Weissenberg number attenuation, the hybrid scheme is more stable than the pure FE alternative for the smooth flow past a cylinder, but less so for the non-smooth contraction flow. The influence of additional strain-rate stabilisation techniques is also analysed and found to be beneficial.