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Journal Articles Journal of Computational Physics Year : 2011

Reduced-order modeling of transonic flows around an airfoil submitted to small deformations

Abstract

A reduced-order model (ROM) is developed for the prediction of unsteady transonic flows past an airfoil submitted to small deformations, at moderate Reynolds number. Considering a suitable state formulation as well as a consistent inner product, the Galerkin projection of the compressible flow Navier–Stokes equations, the high-fidelity (HF) model, onto a low-dimensional basis determined by Proper Orthogonal Decomposition (POD), leads to a polynomial quadratic ODE system relevant to the prediction of main flow features. A fictitious domain deformation technique is yielded by the Hadamard formulation of HF model and validated at HF level. This approach captures airfoil profile deformation by a modification of the boundary conditions whereas the spatial domain remains unchanged. A mixed POD gathering information from snapshot series associated with several airfoil profiles can be defined. The temporal coefficients in POD expansion are shape-dependent while spatial POD modes are not. In the ROM, airfoil deformation is introduced by a steady forcing term. ROM reliability towards airfoil deformation is demonstrated for the prediction of HF-resolved as well as unknown intermediate configurations.
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Dates and versions

hal-03537473 , version 1 (20-01-2022)

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Rémi Bourguet, Marianna Braza, Alain Dervieux. Reduced-order modeling of transonic flows around an airfoil submitted to small deformations. Journal of Computational Physics, 2011, 230 (1), pp.159-184. ⟨10.1016/j.jcp.2010.09.019⟩. ⟨hal-03537473⟩
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