Research Paper#Computational Fluid Dynamics, Reduced Order Modeling, Navier-Stokes Equations🔬 ResearchAnalyzed: Jan 3, 2026 19:54
ROM for Viscous, Incompressible Flow: Exponential Convergence
Published:Dec 27, 2025 11:50
•1 min read
•ArXiv
Analysis
This paper investigates the use of Reduced Order Models (ROMs) for approximating solutions to the Navier-Stokes equations, specifically focusing on viscous, incompressible flow within polygonal domains. The key contribution is demonstrating exponential convergence rates for these ROM approximations, which is a significant improvement over slower convergence rates often seen in numerical simulations. This is achieved by leveraging recent results on the regularity of solutions and applying them to the analysis of Kolmogorov n-widths and POD Galerkin methods. The paper's findings suggest that ROMs can provide highly accurate and efficient solutions for this class of problems.
Key Takeaways
- •Demonstrates exponential convergence of ROM approximations for the Navier-Stokes equations in polygonal domains.
- •Leverages corner-weighted analytic regularity results to achieve exponential convergence.
- •Applies the findings to Kolmogorov n-widths and POD Galerkin methods.
- •Numerical experiments confirm the theoretical results.
Reference
“The paper demonstrates "exponential convergence rates of POD Galerkin methods that are based on truth solutions which are obtained offline from low-order, divergence stable mixed Finite Element discretizations."”