Comparison of Different Formulations for the Numerical Calculation of Unsteady Incompressible Viscoelastic Fluid Flow

In this paper we compare different methods currently used in the stabilization of numerical simulations of time-dependent viscoelastic fluid flows described with the Oldroyd-B and related models. The methods under consideration, based on the separation of newtonian-like components from the stress tensor, are applied to a finite volume analysis of two simple benchmark problems (the plane Poiseuille startup and pulsated flows), for which analytical solutions are known. The relative performances of each method are evaluated regarding stability, accuracy and efficiency.