Adaptive non-intrusive reduced order modeling for compressible flows

An adaptive non-intrusive reduced basis (RB) method based on Gaussian process regression (GPR) is proposed for parametrized compressible flows. Adaptivity is pursued in the offline stage. The reduced basis by proper orthogonal decomposition (POD) is constructed iteratively to achieve a specified tolerance. For GPR, active data selection is used at each iteration, with standard deviation as the error indicator. To improve accuracy for shock-dominated flows, a properly designed simplified problem (SP) is considered as input of the regression models in addition to using parameters directly. Furthermore, a surrogate error model is constructed to serve as an efficient error estimator for the GPR models. Several two- and three-dimensional cases are conducted, including the inviscid nozzle flow, the inviscid NACA0012 airfoil flow and the inviscid M6 wing flow. For all the cases, the trained models are able to make efficient predictions with reasonable accuracy in the online stage. The SP-based approach is observed to result in biased sampling towards transonic regions. The regression models are further applied in sensitivity analysis, from which the solution of the two-dimensional cases are shown to be significantly more sensitive to input parameters than the wing flow. This is consistent to the comparison of convergence histories between the parameter-based and the SP-based models. For cases of high sensitivity, the SP-based approach is superior and can help to significantly reduce the number of required snapshots to achieve a prescribed tolerance.