Adaptive reduced order model of aeroelastic systems using proper orthogonal decomposition

An adaptive reduced order method is considered to simulate unsteady inviscid aeroelastic scenarios for the AGARD 445.6 wing benchmark case and turbulent simulations of a NACA 0012 airfoil. The method is based on Proper Orthogonal Decomposition (POD) and it is constructed using snapshots from a Computational Fluid Dynamics (CFD) solver, which is coupled with a modal structural solver. The method adaptively switches between the full order model (FOM) and the reduced order model (ROM), which is decided on the fly by monitoring a residual estimate. A least-squares minimisation and a Galerkin projection have been used to evolve the ROM, both applied to a residual calculated only on a subset of cells, which significantly further reduces the computational effort. A collocation method for cell selection is performed automatically via LU decomposition. Various implementations of the method are discussed, such as the inclusion of Dual Time-Stepping terms in the ROM iterations, QR reorthogonalisation of POD modes, and the creation of a separate POD for the turbulent equations. Results of forced motion cases and aeroelastic responses to subcritical flow conditions are presented. The outcome is an efficient and robust method with a reduction down to 11% of the CPU time required to compute a full CFD solution