THE SHIFTED PROPER ORTHOGONAL DECOMPOSITION: A MODE DECOMPOSITION FOR MULTIPLE TRANSPORT PHENOMENA

Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kinds 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 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.