The shifted proper orthogonal decomposition: A mode decomposition for multiple transport phenomena

TL;DR

The paper introduces the shifted proper orthogonal decomposition (sPOD), a novel mode decomposition method that effectively captures multiple transport phenomena by incorporating time-dependent shifts, outperforming traditional POD.

Contribution

It extends POD by integrating time-dependent shifts and multiple transport velocities, enabling better modeling of transport-dominated systems.

Findings

sPOD outperforms POD in transport-dominated examples

The method accurately determines multiple transport velocities

sPOD effectively separates different transport phenomena

Abstract

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.