Verification of an Incompressible Viscoelastic Flow Solver Using the Method of Manufactured Solutions for Oldroyd‐B and Giesekus Constitutive Models

Abstract

This study introduces an application of the Method of Manufactured Solutions (MMS) to verify high‐order compact finite‐difference schemes for solving two‐dimensional incompressible viscoelastic flows in the vorticity–stream function formulation. Using the lid‐driven cavity flow as a benchmark, the MMS generates artificial analytical solutions that retain the original equations and boundary conditions, enabling assessment of numerical accuracy, convergence, and stability. The approach is tested on two constitutive models‐Oldroyd‐B and Giesekus‐across Reynolds numbers (), Weissenberg numbers (), solvent viscosity ratios (), and, for the Giesekus constitutive model, mobility parameters (). Results demonstrate a convergence order of approximately 4.5 for most variables, though vorticity exhibits slightly lower orders at higher Reynolds numbers. Mesh refinement consistently reduces errors, confirming the method's robustness across parameters and constitutive models. The study highlights the MMS as a powerful tool for verifying complex viscoelastic flow simulations and provides comprehensive data to ensure reproducibility and future applicability.