ONERA - France
Projection-based Model Order Reduction (pMOR) techniques are widely used to reduce the computational cost of high-fidelity simulations of parametrized partial differential equations. However, these approaches may face limitations in convection-dominated problems, where projection onto linear reduced spaces can lead to stability issues and difficulties in capturing localized dynamical features.
In this presentation, we discuss a collocation-based Model Order Reduction (cMOR) strategy as an alternative to classical projection-based approaches. The method retains the standard offline–online paradigm: a reduced basis is first constructed from high-fidelity snapshots, while the reduced solution is computed in the online stage by enforcing the governing equations only at a limited set of collocation points selected through hyper-reduction techniques. The resulting formulation preserves the structure of the underlying high-fidelity scheme while significantly reducing computational cost.
To enhance the expressive power of reduced models, we explore the use of nonlinear approximation manifolds obtained through neural-network-based corrections of the reduced representation. This approach enables the reduced model to capture complex nonlinear solution structures that are difficult to approximate within classical linear reduced spaces.
We then present applications of the collocation-based framework to problems arising in computational fluid dynamics on complex and evolving geometries. In particular, we consider simulations performed on moving Chimera grids, where overlapping mesh blocks allow the efficient treatment of dynamic geometries and parametric configurations. The combination of cMOR with this flexible discretization framework enables accurate and efficient reduced simulations even in challenging convection-dominated scenarios.
These results illustrate the potential of collocation-based reduced-order models combined with nonlinear approximation strategies for tackling complex fluid dynamics problems on evolving computational meshes.