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