Publications

2026

• Reduced order modelling of Hopf bifurcations for the Navier-Stokes equations through invariant manifolds
  
  • Colombo Alessio
  • Vizzaccaro Alessandra
  • Touzé Cyril
  • de F. Stabile André
  • Pastur Luc
  • Frangi Attilio
  Physical Review E, American Physical Society (APS), 2026, 113 (3), pp.034202. 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. (10.1103/w6z2-m5wk)
  DOI : 10.1103/w6z2-m5wk