Research on the impact of shock wave to extensionality of POD method

In this paper, flow reconstruction accuracy and flow prediction capability of discontinuous transonic flow field by means of proper orthogonal decomposition (POD) method is studied. The ability to reconstruct and predict flow flied is called extensionality of POD method in this paper. Although, only using a few modes, we can capture the information of subsonic flow field. When it counters the shock wave, the smoothness of the solution near the shock wave cannot be guaranteed. The modal coefficients are interpolated or extrapolated and different modal components are superposed to realize the prediction of the flow field beyond the snapshot sets. Results show that compared with the subsonic flow, the transonic flow with shock wave requires more POD modes to reach a comparative reconstruction accuracy. When a shock wave exists, the interpolation prediction ability is acceptable. However, large errors exist in extrapolation, and increasing the number of POD modes cannot effectively improve the prediction accuracy of the flow field.