A Hybrid Discretize-then-Project Reduced Order Model for Turbulent Flows on Collocated Grids with Data-Driven Closure
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| Format: | Preprint |
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2026
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| author | Rooholamin, Nadim Bakhshaei, Kabir Stabile, Giovanni |
| author_facet | Rooholamin, Nadim Bakhshaei, Kabir Stabile, Giovanni |
| contents | This study presents a hybrid reduced-order modeling (ROM) framework for turbulent incompressible flows on collocated finite volume grids. The methodology employs the "discretize-then-project" consistent flux strategy, which ensures mass conservation and pressure-velocity coupling without requiring auxiliary stabilization like boundary control or pressure stabilization techniques. However, because standard Galerkin projection fails to yield physically consistent results for the turbulent viscosity field, a hybrid strategy is adopted: velocity and pressure are resolved via intrusive projection, while the turbulent viscosity is reconstructed using a non-intrusive data-driven closure. We evaluate three neural network architectures, Multilayer Perceptron (MLP), Transformers, and Long Short-Term Memory (LSTM), to model the temporal evolution of the viscosity coefficients. Validated against a 3D Large Eddy Simulation of a lid-driven cavity, the LSTM-based closure demonstrates superior performance in capturing transient dynamics, achieving relative errors of 0.7\% for velocity and 4\% for turbulent viscosity. The resulting framework effectively combines the mathematical rigor of the consistent flux formulation with the adaptability of deep learning for turbulence modeling. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_18817 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Hybrid Discretize-then-Project Reduced Order Model for Turbulent Flows on Collocated Grids with Data-Driven Closure Rooholamin, Nadim Bakhshaei, Kabir Stabile, Giovanni Numerical Analysis Fluid Dynamics 65M60, 65N35 This study presents a hybrid reduced-order modeling (ROM) framework for turbulent incompressible flows on collocated finite volume grids. The methodology employs the "discretize-then-project" consistent flux strategy, which ensures mass conservation and pressure-velocity coupling without requiring auxiliary stabilization like boundary control or pressure stabilization techniques. However, because standard Galerkin projection fails to yield physically consistent results for the turbulent viscosity field, a hybrid strategy is adopted: velocity and pressure are resolved via intrusive projection, while the turbulent viscosity is reconstructed using a non-intrusive data-driven closure. We evaluate three neural network architectures, Multilayer Perceptron (MLP), Transformers, and Long Short-Term Memory (LSTM), to model the temporal evolution of the viscosity coefficients. Validated against a 3D Large Eddy Simulation of a lid-driven cavity, the LSTM-based closure demonstrates superior performance in capturing transient dynamics, achieving relative errors of 0.7\% for velocity and 4\% for turbulent viscosity. The resulting framework effectively combines the mathematical rigor of the consistent flux formulation with the adaptability of deep learning for turbulence modeling. |
| title | A Hybrid Discretize-then-Project Reduced Order Model for Turbulent Flows on Collocated Grids with Data-Driven Closure |
| topic | Numerical Analysis Fluid Dynamics 65M60, 65N35 |
| url | https://arxiv.org/abs/2601.18817 |