Reduced order modeling of transonic flows around an airfoil

Rémi Bourguet Mariana Braza (IMFT Toulouse) Alain Dervieux (INRIA, BP93, 06902 Sophia-Antipolis, France)

Article in Journal of Computational Physics, 2011 (26 pages)

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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@article{BBD11,
  author = {Bourguet, R. and Braza, M. and Dervieux, A.},
  title = {Reduced order modeling of  transonic flows around an airfoil},
  journal = {Journal of Computational Physics},
  volume = {230},
  number = {1},
  pages = {159-184},
  year = 2011
}