Abstract
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.
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Funding
Open access funding provided by Scuola Internazionale Superiore di Studi Avanzati - SISSA within the CRUI-CARE Agreement. We acknowledge the support provided by the European Research Council Executive Agency by the Consolidator Grant project AROMA-CFD “Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics” - GA 681447, H2020-ERC CoG 2015 AROMA-CFD, PI G. Rozza, and INdAM-GNCS 2019-2020 projects. This work was also partially supported by the US National Science Foundation through grant DMS-1953535. A. Quaini acknowledges support from the Radcliffe Institute for Advanced Study at Harvard University where she has been a 2021–2022 William and Flora Hewlett Foundation Fellow.
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Communicated by: Olga Mula
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Hess, M.W., Quaini, A. & Rozza, G. A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation. Adv Comput Math 49, 22 (2023). https://doi.org/10.1007/s10444-023-10016-4
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DOI: https://doi.org/10.1007/s10444-023-10016-4
Keywords
- Spectral element method
- Computational fluid dynamics
- Model order reduction
- Dynamic mode decomposition
- Manifold interpolation