Closure of nonlinear frequency-domain reduced-order models for unsteady flows
Closure of nonlinear frequency-domain reduced-order models for unsteady flows
In this work, we utilise space-time basis functions derived from Spectral Proper Orthogonal Decomposition (SPOD) to construct a frequency-domain reduced-order model (ROM) that preserves the intrinsic spatio-temporal correlations of unsteady flows. The ROM is formulated as a system of nonlinear algebraic equations, where the solutions correspond to amplitude coefficients of SPOD modes, determined by minimising the sum of the squared residual norms to enforce momentum conservation. However, the frequency-domain ROM obtained from Galerkin projection may lead to significant discrepancies in flow predictions due to the truncation of SPOD modes. We introduce a generalised closure framework that augments the ROM by incorporating the influence of truncated SPOD modes. This framework employs a hierarchical strategy to construct linear closure models with constant, mode-dependent and sparsity-promoting eddy-
viscosity coefficients. The proposed models are validated using a periodic flow inside a two-dimensional lid-driven cavity at Re=10000. All closure mod-
els significantly improve the accuracy of ROM prediction in terms of energy dissipation rate and energy input rate. The sparsity-promoting technique identifies a family of closure models with varying fidelity, with the most accurate model matching the results obtained from Direct Numerical Simulation. The proposed approach shows great potential to enhance the ROM’s capacity to accurately capture the dynamical behaviour of non-stationary flows.
closure, reduced-order model (ROM), Periodic flow, sparsity constrained optimization
859-864
Li, Xiaodong
a471b477-f562-422e-94be-706100614bad
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
22 September 2025
Li, Xiaodong
a471b477-f562-422e-94be-706100614bad
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Li, Xiaodong and Lasagna, Davide
(2025)
Closure of nonlinear frequency-domain reduced-order models for unsteady flows.
Hickel, Stefan and Salvetti, Maria Vittoria
(eds.)
In Proceedings of the 15th ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements.
.
(doi:10.5281/zenodo.17280519).
Record type:
Conference or Workshop Item
(Paper)
Abstract
In this work, we utilise space-time basis functions derived from Spectral Proper Orthogonal Decomposition (SPOD) to construct a frequency-domain reduced-order model (ROM) that preserves the intrinsic spatio-temporal correlations of unsteady flows. The ROM is formulated as a system of nonlinear algebraic equations, where the solutions correspond to amplitude coefficients of SPOD modes, determined by minimising the sum of the squared residual norms to enforce momentum conservation. However, the frequency-domain ROM obtained from Galerkin projection may lead to significant discrepancies in flow predictions due to the truncation of SPOD modes. We introduce a generalised closure framework that augments the ROM by incorporating the influence of truncated SPOD modes. This framework employs a hierarchical strategy to construct linear closure models with constant, mode-dependent and sparsity-promoting eddy-
viscosity coefficients. The proposed models are validated using a periodic flow inside a two-dimensional lid-driven cavity at Re=10000. All closure mod-
els significantly improve the accuracy of ROM prediction in terms of energy dissipation rate and energy input rate. The sparsity-promoting technique identifies a family of closure models with varying fidelity, with the most accurate model matching the results obtained from Direct Numerical Simulation. The proposed approach shows great potential to enhance the ROM’s capacity to accurately capture the dynamical behaviour of non-stationary flows.
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Published date: 22 September 2025
Venue - Dates:
The 15th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements, Sheraton Dubrovnik Riviera Hotel, Dubrovnik, Croatia, 2025-09-22 - 2025-09-24
Keywords:
closure, reduced-order model (ROM), Periodic flow, sparsity constrained optimization
Identifiers
Local EPrints ID: 508677
URI: http://eprints.soton.ac.uk/id/eprint/508677
PURE UUID: 776e4d04-901f-4651-9928-15db527a04a4
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Date deposited: 29 Jan 2026 17:44
Last modified: 31 Jan 2026 07:45
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Contributors
Author:
Xiaodong Li
Editor:
Stefan Hickel
Editor:
Maria Vittoria Salvetti
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