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Preprint 22-2015

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

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Author(s) : Julius Reiss , Philipp Schulze , Jörn Sesterhenn , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 22-2015

MSC 2000

65Z05 Applications to physics
35Q35 Other equations arising in fluid mechanics

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 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.

Keywords : transport phenomena, model reduction, mode decomposition, shifted proper orthogonal decomposition, proper orthogonal decomposition, principal component analysis

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