Using proper orthogonal decomposition to model off-reference flow conditions

• POD results are shown using basis functions obtained through interpolation.
• The effect of interpolation order is shown for subsonic and transonic flows.
• Energy variation is used to determine necessary number of basis functions.

Proper orthogonal decomposition results from subsonic and transonic flow regimes are presented, and the full-order model is compared with the reduced-order models. The reduced-order models use basis functions generated for on- and off-reference flow conditions. For on-reference flow conditions, proper orthogonal decomposition of the full-order model is performed to generate the basis functions. For off-reference flow conditions, basis functions are obtained through interpolating among basis functions corresponding to bracketing flow conditions. Interpolation is performed on a tangent space to a Grassmann manifold. This paper evaluates the accuracy of POD at off-reference flow conditions for subsonic and transonic flow regimes. The results show that interpolation yields good results for the subsonic cases, but the accuracy of the transonic cases is considerably lower. Furthermore, the energy spectrum is used to assess the necessary number of basis functions. It is demonstrated that in order to determine the number of basis functions, it is better to assess the variation of individual energy values, as opposed to the cumulative energy values.