Data-driven Optimization for the Evolve-Filter-Relax regularization of convection-dominated flows
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912321794736128 |
|---|---|
| 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 |