A comparison of four implementations of the log-conformation formulation for viscoelastic fluid flows

We compare four finite element implementations of a log-conformation formulation for the numerical solution of viscoelastic fluid flow problems. These formulations essentially differ the treatment of the advective term. The first formulation was introduced in Fattal and Kupferman (2005) [1] while the second one, much simpler to implement, was proposed by Coronado et al. (2007) [2]. We then introduce the two variants of this last formulation. In the first one, a special treatment is done to the computation of the advective term u⋅∇es which is more accurate than the one described in Coronado et al. (2007) [2]. In the second variant, we show how es and ∇es can be computed in order to allow a complete linearization of the constitutive equation and its solution by Newton’s method. A comparative study of these four formulations is done on the benchmark problem of the flow of an Oldroyd-B fluid past a circular cylinder in a rectangular channel.