The motivation for the present work is to develop a reduced order model (ROM) for gradient based aerodynamic shape optimization. The fluid Euler equations or full order model (FOM) is converted to a reduced Newton iteration by using the Petrov-Galerkin projection. The reduced order basis (ROB) are extracted by Proper Orthogonal Decomposition (POD) from snapshots collected of the fluid state, along the optimization trajectory. Similarly, the reduced gradient formulation is derived by projecting the FOM state onto the subspace spanned by ROBs. The residual of reduced Newton iteration is used as an indicator to update the snapshots and ROB. The ROM is demonstrated for a subsonic inverse design problem and for airfoil drag minimization at transonic Mach numbers. The results suggest that the constructed ROM is capable of aerodynamic shape optimization while reducing the number of FOM queries with respect to an adjoint gradient based optimization framework. The reduction in computation cost is over one order of magnitude for the subsonic case; however, efficiency deteriorates for the transonic problem, exhibiting a reduction in computational time of about one-third with respect to an optimization using the FOM.
|Title of host publication||AIAA Scitech 2019 Forum|
|Publisher||American Institute of Aeronautics and Astronautics Inc, AIAA|
|Publication status||Published (in print/issue) - 6 Jan 2019|
|Event||AIAA Scitech Forum, 2019 - San Diego, United States|
Duration: 7 Jan 2019 → 11 Jan 2019
|Conference||AIAA Scitech Forum, 2019|
|Period||7/01/19 → 11/01/19|