Data-driven closure of projection-based reduced order models for unsteady compressible flows

A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction obtained via Galerkin Petrov–Galerkin projection the non-conservative Navier–Stokes equations. The latter approach implemented using least-squares (LSPG) technique present methodology allows pre-computation (i.e., not requiring hyper-reduction) both LSPG coefficients. Closure performed by adding linear non-linear coefficients original ROMs minimizing error with respect POD modes. In further reduce computational cost ROMs, an accelerated greedy missing point estimation (MPE) hyper-reduction method employed. canonical cylinder flow first analyzed serves as a benchmark. second problem studied consists turbulent over plunging airfoil undergoing deep dynamic stall. For cases, regularization required iterative Tikhonov proposed. case, are low in intrusiveness, capable providing results excellent agreement full model. Regularization calibrated also straightforward for this case. On other hand, stall significantly more challenging, specially when only used. Results show that calibration outperform their counterparts basis fewer reconstruction. However, determining correct level complicated Hyper-reduced good combined appropriate sized basis.