The performance of proper orthogonal decomposition in discontinuous flows

- The proper orthogonal decomposition (POD) modes have special pattern for flow existing shock wave.
- The reason why reconstructing transonic flow needs more POD modes is explained.
- POD combined with interpolation has good prediction ability for transonic flow.
- POD combined with extrapolation does not have prediction ability for transonic flow.

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. Although linear superposition of “high frequency waves” in different POD modes can achieve the reconstruction of 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.