Calibration of projection-based compressible flow reduced order models with quadratic manifold approximation

Reduced order modeling is a popular approach that generates surrogate models by combining physics-based or data-driven techniques with a lower dimensional representation from training generated data. Linear reduction approximations such as proper orthogonal decomposition (POD) are commonly used in model order reduction. However, complex flow problems could require hundreds, if not thousands, of modes to produce an accurate reduced order model (ROM). Recently, nonlinear techniques have emerged as a solution to this shortcoming. In principle, nonlinear methods allow for a much smaller basis. Unfortunately, most nonlinear methods usually come with issues that undermine their viability to large scale problems. In this work, a quadratic manifold approach is implemented and analyzed to solved unsteady compressible flow problems. In particular, this techniques allows for pre-computation of the ROM coefficients when a non-conservative compressible Navier-Stokes equation formulation is used. Moreover, a data-driven calibration of the ROM is applied to enhance accuracy and stability.