Abstract Simulating viscoelastic fluids at high Weissenberg numbers is challenging due to numerical instabilities, especially in flows with singularities. The natural stress formulation (NSF) is a robust technique designed to overcome these issues. Separately, the generalized Phan-Thien and Tanner (gPTT) model offers enhanced rheological flexibility by using the Mittag-Leffler function. This work develops and validates an in-house, finite-difference NSF-gPTT solver. The method is first validated against the traditional HiG-Flow solver in channel flow and 1: 4 sudden expansion geometries, showing excellent agreement for velocity/stress profiles and vortex reattachment lengths. We then apply the framework to the L-shaped channel benchmark, which features a re-entrant corner. The NSF-gPTT solver remains stable and accurate up to a Weissenberg number (Wi) of 100. The results reveal a counter-intuitive decrease in the peak of the first normal stress difference (N₁ N 1) at the corner with increasing Wi, a direct result of the gPTT model’s shear-thinning. Furthermore, we demonstrate the NSF’s stability by showing that at Wi=100 W i = 100, the internal conformation tensor trace grows to 100 ≈ 100, while the elastic stress trace remains small (0. 48 ≈ 0. 48). This study demonstrates that the NSF-gPTT formulation is a stable and powerful tool for probing complex viscoelastic phenomena in high- Wi regimes.
Neto et al. (2026) studied this question.