A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation

• Published in: Advances in computational mathematics Vol. 49; no. 2
• Main Authors: Hess, Martin W., Quaini, Annalisa, Rozza, Gianluigi
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2023; Springer Nature B.V
• Subjects: Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Grashof number; Interpolation; Manifolds; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Model reduction; Navier-Stokes equations; Partial differential equations; Proper Orthogonal Decomposition; Time dependence; Visualization; 35Q35 65M22 76E30 76M22; Spectral element method; Model order reduction; Computational fluid dynamics; Manifold interpolation; Dynamic mode decomposition
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-023-10016-4

This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition, and manifold interpolation, the proposed approach allows to accurately recover field solutions from a few large-scale simulations. Numerical experiments for the Rayleigh-Bénard cavity problem show the effectiveness of such multi-step procedure in two parametric regimes, i.e., medium and high Grashof number. The latter regime is particularly challenging as it nears the onset of turbulent and chaotic behavior. A major advantage of the proposed method in the context of time-periodic solutions is the ability to recover frequencies that are not present in the sampled data.