Data-driven Optimization for the Evolve-Filter-Relax regularization of convection-dominated flows

Fuente: arXiv
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Main Authors: Ivagnes, Anna, Strazzullo, Maria, Girfoglio, Michele, Iliescu, Traian, Rozza, Gianluigi
Format: Preprint
Published: 2025
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author Ivagnes, Anna
Strazzullo, Maria
Girfoglio, Michele
Iliescu, Traian
Rozza, Gianluigi
author_facet Ivagnes, Anna
Strazzullo, Maria
Girfoglio, Michele
Iliescu, Traian
Rozza, Gianluigi
contents Numerical stabilization techniques are often employed in under-resolved simulations of convection-dominated flows to improve accuracy and mitigate spurious oscillations. Specifically, the evolve--filter--relax (EFR) algorithm is a framework which consists in evolving the solution, applying a filtering step to remove high-frequency noise, and relaxing through a convex combination of filtered and original solutions. The stability and accuracy of the EFR solution strongly depend on two parameters, the filter radius $δ$ and the relaxation parameter $χ$. Standard choices for these parameters are usually fixed in time, and related to the full order model setting, i.e., the grid size for $δ$ and the time step for $χ$. The key novelties with respect to the standard EFR approach are: (i) time-dependent parameters $δ(t)$ and $χ(t)$, and (ii) data-driven adaptive optimization of the parameters in time, considering a fully-resolved simulation as reference. In particular, we propose three different classes of optimized-EFR (Opt-EFR) strategies, aiming to optimize one or both parameters. The new Opt-EFR strategies are tested in the under-resolved simulation of a turbulent flow past a cylinder at $Re=1000$. The Opt-EFR proved to be more accurate than standard approaches by up to 99$\%$, while maintaining a similar computational time. In particular, the key new finding of our analysis is that such accuracy can be obtained only if the optimized objective function includes: (i) a global metric (as the kinetic energy), and (ii) spatial gradients' information.
format Preprint
id arxiv_https___arxiv_org_abs_2501_03933
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Data-driven Optimization for the Evolve-Filter-Relax regularization of convection-dominated flows
Ivagnes, Anna
Strazzullo, Maria
Girfoglio, Michele
Iliescu, Traian
Rozza, Gianluigi
Numerical Analysis
Optimization and Control
Fluid Dynamics
Numerical stabilization techniques are often employed in under-resolved simulations of convection-dominated flows to improve accuracy and mitigate spurious oscillations. Specifically, the evolve--filter--relax (EFR) algorithm is a framework which consists in evolving the solution, applying a filtering step to remove high-frequency noise, and relaxing through a convex combination of filtered and original solutions. The stability and accuracy of the EFR solution strongly depend on two parameters, the filter radius $δ$ and the relaxation parameter $χ$. Standard choices for these parameters are usually fixed in time, and related to the full order model setting, i.e., the grid size for $δ$ and the time step for $χ$. The key novelties with respect to the standard EFR approach are: (i) time-dependent parameters $δ(t)$ and $χ(t)$, and (ii) data-driven adaptive optimization of the parameters in time, considering a fully-resolved simulation as reference. In particular, we propose three different classes of optimized-EFR (Opt-EFR) strategies, aiming to optimize one or both parameters. The new Opt-EFR strategies are tested in the under-resolved simulation of a turbulent flow past a cylinder at $Re=1000$. The Opt-EFR proved to be more accurate than standard approaches by up to 99$\%$, while maintaining a similar computational time. In particular, the key new finding of our analysis is that such accuracy can be obtained only if the optimized objective function includes: (i) a global metric (as the kinetic energy), and (ii) spatial gradients' information.
title Data-driven Optimization for the Evolve-Filter-Relax regularization of convection-dominated flows
topic Numerical Analysis
Optimization and Control
Fluid Dynamics
url https://arxiv.org/abs/2501.03933