Improvement of Reduced Order Modeling based on Proper Orthogonal Decomposition

Michel Bergmann (1, 2) , Charles-Henri Bruneau (1, 2) , Angelo Iollo (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 MC2 - Modélisation, contrôle et calcul

This report focuses on improving the stability as well as the approximation properties of Reduced Order Models (ROM) based on Proper Orthogonal Decomposition (POD). The ROM is obtained by seeking a solution belonging to the POD subspace and that at the same time minimizes the Navier-Stokes residuals. We propose a modified ROM that directly incorporates the pressure term in the model. The ROM is then stabilized making use of a method based on the fine scale equations. An improvement of the POD solution subspace is performed thanks to an hybrid method that couples direct numerical simulations and reduced order model simulations. The methods proposed are tested on the two-dimensional confined square cylinder wake flow in laminar regime.

Mots clés: Proper Orthogonal Decomposition; Reduced Order Model; Stabilization; Functional subspace

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Michel Bergmann, Charles-Henri Bruneau, Angelo Iollo. Improvement of Reduced Order Modeling based on Proper Orthogonal Decomposition. [Research Report] RR-6561, INRIA. 2008, pp.37. ⟨inria-00288415v2⟩