Stable Numerical Methods for Viscoelastic Giesekus Model
Published:Dec 28, 2025 08:10
•1 min read
•ArXiv
Analysis
This paper addresses the challenges of numerically solving the Giesekus model, a complex system used to model viscoelastic fluids. The authors focus on developing stable and convergent numerical methods, a significant improvement over existing methods that often suffer from accuracy and convergence issues. The paper's contribution lies in proving the convergence of the proposed method to a weak solution in two dimensions without relying on regularization, and providing an alternative proof of a recent existence result. This is important because it provides a reliable way to simulate these complex fluid behaviors.
Key Takeaways
- •Develops stable and convergent numerical methods for the Giesekus model.
- •Proves convergence to a weak solution in 2D without regularization.
- •Provides an alternative proof of a recent existence result.
- •Verifies the practicality of the method through numerical experiments.
Reference
“The main goal is to prove the (subsequence) convergence of the proposed numerical method to a large-data global weak solution in two dimensions, without relying on cut-offs or additional regularization.”