A Hybrid Discretize-then-Project Reduced Order Model for Turbulent Flows on Collocated Grids with Data-Driven Closure

Fuente: arXiv
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Main Authors: Rooholamin, Nadim, Bakhshaei, Kabir, Stabile, Giovanni
Format: Preprint
Published: 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
id 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