Stabilization of an open-source finite-volume solver for viscoelastic fluid flows

- A robust viscoelastic solver is presented using the OpenFOAM® toolbox.
- The solver is tested on benchmark flows for an Oldroyd-B fluid.
- New results for the 4:1 planar contraction are presented.
- Steady and time-dependent flows are analyzed.

In this work, we modify the viscoelastic solver available in the OpenFOAM® toolbox (Favero et al., 2010), in order to improve its stability for differential-type constitutive equations. The Oldroyd-B constitutive equation is solved using the log-conformation approach and the high-resolution schemes used to discretize the convective terms are handled with a component-wise and deferred correction approach. The pressure-velocity coupling is ensured using the SIMPLEC algorithm, and a new stress-velocity coupling term is also introduced. We demonstrate that the new solver is second-order accurate, both in space and time, by assessing the performance in problems with known analytical solution and using Richardson's extrapolation. The solver is further tested on the 4:1 planar contraction benchmark problem using an Oldroyd-B fluid (β = 1/9) at low Reynolds number flow conditions (Re = 0.01), considering a wide range of Deborah numbers, 0 ≤ De ≤ 12. A good agreement with reference works is observed at low De, as well as with an in-house viscoelastic flow solver. At higher De, the vortex dynamics is essentially controlled by the singularity region in the re-entrant corner of the contraction, revealing a significant dependence of the numerical results on the mesh resolution. The corner vortex dynamics is also analyzed, from the flow startup at several De, providing new accurate data on the transient behavior of this problem. In summary, this work provides a robust open-source solver for viscoelastic flows, as well as new data on an old problem, which has still open questions and challenges.