Enhancing coupled numerical simulations of viscoelastic flows through physical property analysis

Polymeric fluids exhibit complex viscoelastic behavior governed by nonlinear constitutive equations. Considering the full mathematical formulation is essential for accurately representing the behavior of these fluids. Numerical simulations with viscoelastic fluids can face stability and convergence challenges, especially when modeling real-world polymer processing test cases. To address these issues, a coupled solver for multi-mode viscoelastic flows was developed within the foam-extend framework, where pressure, velocity, and a selected viscoelastic mode are solved together in a single block system, while the remaining modes follow a segregated procedure. A key question is how to select the mode to include in the block system, as this choice can significantly affect both computational efficiency and solution accuracy. This study systematically investigates the impact of coupling each individual mode in a six-mode fluid. The results highlight how mode selection influences convergence time and overall solution quality. Additionally, a novel convergence assessment that was recently proposed is further tested. It is based on physical flow characteristics rather than solely on numerical residuals. Specifically, the variables such as total pressure drop and outlet flow distribution in three distinct zones evolution are tracked. This approach avoids inconsistencies caused by different residual normalizations in segregated and fully coupled solvers and provides a more reliable measure of convergence across various simulation strategies.