A POD-DEIM Reduced Order Model with deforming mesh for aeroelastic applications ; Un POD-DEIM modèle d'ordre réduit avec maillage déformable pour des applications aéroélastiques

International audience ; Reduced-order models (ROMs) of nonlinear dynamical systems are essential for broadening the scope of high-fidelity non linear CFD design optimizations or aeroelastic investigations. The wide variety of fluid dynamics ROMs reported in literature shares the aim of reducing the dimensionality of dynamical systems by performing a projection of the governing equations onto a basis that may be often constructed via the Proper Orthogonal Decomposition (POD). Unfortunately, the relevance of POD is still an open question for aeroelastic applications, involving the deformation of the domain. Moreover, when addressing real-life applications, the non-linear compressible Navier-Stokes equations have to be considered, resulting in an additional difficulty. In the present work, we propose a ROM based on the classical Galerkin projection onto a basis contructed via the index-based POD. The discrete empirical interpolation method (DEIM) is adopted in order to efficiently deal with the compressible Navier-Stokes equations non-linearities. Numerical tests have been carried out to evaluate the performance of the ROM. First, we validate the classical POD-DEIM technique for a time-dependent and slightly compressible flow around a NACA 0012 airfoil with high incidence. Then, the POD-DEIM ROM is used to reproduce the solution of a highfidelity model based on the Arbitrary Lagrangian-Eulerian (ALE) formulation combined with a deforming grid for a flow around an oscillating supercritical airfoil. On the basis of the achieved results, we highlight the limits and the strengths of the proposed technique. ; Les modèles d'ordre réduit (MOR) des systèmes dynamiques non-linéaires constituent des outils indispensables pour traiter efficacement des études paramétriques ou d'optimisation basées sur des calculs CFD haute-fidélité. La grande variété de MOR pour l'aérodynamique présente dans la littérature a comme but de réduire la dimension du système dynamique en projetant les équations du modèle haute fidélité sur une base ...