The shifted proper orthogonal decomposition: A mode decomposition for multiple transport phenomena
For researchers in model reduction, this method addresses the bottleneck of handling multiple transport phenomena, though it is an incremental extension of POD.
The paper introduces the shifted proper orthogonal decomposition (sPOD) for model reduction of transport-dominated phenomena, demonstrating superior performance over standard POD on 1D and 2D test examples.
Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kind of systems. It extends the proper orthogonal decomposition (POD) by introducing time-dependent shifts of the snapshot matrix. The approach, called shifted proper orthogonal decomposition (sPOD), features a determination of the {\it multiple} transport velocities and a separation of these. One- and two-dimensional test examples reveal the good performance of the sPOD for transport-dominated phenomena and its superiority in comparison to the POD.