Application of proper orthogonal decomposition to the discrete Euler equations

The response of a uid moving above a panel to localized oscillation of the panel is predicted using reduced-order modelling (ROM) with the proper orthogonal decomposition technique. The ow is assumed to be inviscid and is modelled with the Euler equations. These non-linear equations are discretized with a total-variation diminishing algorithm and are projected onto an energy-optimal subspace de ned by an energy-threshold criterion applied to a modal representation of time series data. Results are obtained for a bump oscillating in a Mach 1.2 ow. ROM is found to reduce the degrees of freedom necessary to simulate the ow eld by three orders of magnitude while preserving solution accuracy. Other observed bene ts of ROM include increased allowable time step and robustness to variation of oscillation amplitude