Improving the Numerical Stability of Steady-State Differential Viscoelastic Flow Solvers in OpenFOAM$^{\textregistered }$

Abstract

This work reports the developments made in improving the numerical stability of the viscoelastic solvers available in the open-source finite volume computational library $OpenFOAM^{\textregistered }$. For this purpose, we modify the usual both-side diffusion (BSD) technique, using a new approach to discretize the explicit diffusion operator. Calculations performed with the new solver, for two benchmark 2D case studies of an upper-convected Maxwell (UCM) fluid, are presented and compared with literature results, namely the 4:1 planar contraction flow and the flow around a confined cylinder. In the 4:1 planar contraction flow, the corner vortex size predictions agree well with the literature, and a relative error below $5.3 \%$ is obtained for $De \le 5$. In the flow around a confined cylinder, the predictions of the drag coefficient on the cylinder are similar to reference data, with a relative error below $0.16 \%$ for $De \le 0.9$.