Steady supersonic flow-field predictions using proper orthogonal decomposition technique

In the present study, the proper orthogonal decomposition (POD) approach is coupled with the interpolation-extrapolation and the marching extrapolation procedure to predict the steady supersonic flow field by ensembling the data obtained from the numerical simulations. The procedure developed, uses an ensemble data for a given parametric variation and then it is applied to predict the steady flow field that has not been included in the parametric variations. The problem of axisymmetric surface-mounted triangular protuberance is used to demonstrate the efficiency and the accuracy of the proposed strategy. The Mach number and the protuberance height are used as the two parameters, for which the POD snapshots are collected by varying these parameters in the specified interval. The direct POD interpolation procedure performs accurately and efficiently when the flow field is reconstructed for the parameter whose value lies inside the snapshot ensembling interval. In order to predict the flow field outside the snapshot ensembling interval the direct POD extrapolation procedure is used. It is found that, in order to predict the complete supersonic steady-state flow field accurately, using POD interpolation or extrapolation procedure, the RMS deviations in the components of the reconstructed field from the ensembled data should be <1%. The direct POD extrapolation procedure is quite accurate near the ensembling interval but the predictions are inaccurate as one moves farther from the ensembling interval. A marching POD extrapolation (MPODE) procedure is also suggested which results in ameliorating the overall RMS error by 50% compared with the direct POD extrapolation procedure.