Reduced order modelling of Hopf bifurcations for the Navier-Stokes equations through invariant manifolds
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915586978611200 |
|---|---|
| author | Colombo, Alessio Vizzaccaro, Alessandra Touzé, Cyril Stabile, André de F. Pastur, Luc Frangi, Attilio |
| author_facet | Colombo, Alessio Vizzaccaro, Alessandra Touzé, Cyril Stabile, André de F. Pastur, Luc Frangi, Attilio |
| contents | This work introduces a parametric simulation-free reduced order model for incompressible flows undergoing a Hopf bifurcation, leveraging the parametrisation method for invariant manifolds. Unlike data-driven approaches, this method operates directly on the governing equations, eliminating the need for full-order simulations. The proposed model is computed at a single value of the bifurcation parameter yet remains valid over a range of values. The approach systematically constructs an invariant manifold and embedded dynamics, providing an accurate and efficient reduction of the original system. The ability to capture pre-critical steady states, the bifurcation point, and post-critical limit cycle oscillations is demonstrated by a strong agreement between the reduced order model and full order simulations, while achieving significant computational speed-up. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26542 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduced order modelling of Hopf bifurcations for the Navier-Stokes equations through invariant manifolds Colombo, Alessio Vizzaccaro, Alessandra Touzé, Cyril Stabile, André de F. Pastur, Luc Frangi, Attilio Computational Engineering, Finance, and Science Dynamical Systems This work introduces a parametric simulation-free reduced order model for incompressible flows undergoing a Hopf bifurcation, leveraging the parametrisation method for invariant manifolds. Unlike data-driven approaches, this method operates directly on the governing equations, eliminating the need for full-order simulations. The proposed model is computed at a single value of the bifurcation parameter yet remains valid over a range of values. The approach systematically constructs an invariant manifold and embedded dynamics, providing an accurate and efficient reduction of the original system. The ability to capture pre-critical steady states, the bifurcation point, and post-critical limit cycle oscillations is demonstrated by a strong agreement between the reduced order model and full order simulations, while achieving significant computational speed-up. |
| title | Reduced order modelling of Hopf bifurcations for the Navier-Stokes equations through invariant manifolds |
| topic | Computational Engineering, Finance, and Science Dynamical Systems |
| url | https://arxiv.org/abs/2510.26542 |