Calibration of projection-based reduced-order models for unsteady compressible flows

An analysis of calibration for reduced-order models (ROMs) is presented in this work. The Galerkin and least-squares Petrov-Galerkin (LSPG) methods are tested on compressible flows involving a disparity temporal scales. A novel strategy proposed the LSPG method two test cases analyzed. first consists subsonic airfoil flow where boundary layer instabilities responsible trailing-edge noise generation second comprises supersonic with transient period detached shock wave propagates upstream at same time that shock-vortex interaction occurs trailing edge. Results show produces stable long-time accurate ROMs both investigated. impact hyper-reduction via an accelerated greedy missing point estimation (MPE) algorithm. For case investigated, solutions obtained good comparison those by full order model. However, features need to be properly captured sampled points MPE method. Otherwise, dynamics moving not fully recovered. different time-marching schemes also assessed and, differently than reported literature, shown more computed when non-conservative form Navier-Stokes equations solved. case, (without hyper-reduction) capture overall oblique waves along airfoil. trailing-edge, ROM able high-frequency fluctuations from vortex shedding while presents dissipative solution, being recover dynamics.