Numerical study of the square-root conformation tensor formulation for confined and free-surface viscoelastic fluid flows

We present a numerical study of a stabilization method for computing confined andfree-surface flows of highly elastic viscoelastic fluids. In this approach, the constitutiveequation based on the conformation tensor, which is used to define the viscoelasticmodel, is modified introducing an evolution equation for the square-root conformationtensor. Both confined and free-surface flows are considered, using two differentnumerical codes. A finite volume method is used for confined flows and a finitedifference code developed in the context of the marker-and-cell method is used forconfined and free-surface flows. The implementation of the square-root formulationwas performed in both numerical schemes and discussed in terms of its ability andefficiency to compute steady and transient viscoelastic fluid flows. The numericalresults show that the square-root formulation performs efficiently in the testedbenchmark problems at high-Weissenberg number flows, such as the lid-driven cavityflow, the flow around a confined cylinder, the cross-slot flow and the impacting dropfree surface problem