Effects of spatial resolution of the data on dynamic mode decomposition and its quantitative analysis

Jeonghoon Lee (1, 2) , Laurent Zimmer (3) , Takeshi Saito (4) , Shinji Nakaya (2) , Mitsuhiro Tsue (2)

1 Tokyo University of Science [Tokyo]
2 Department of Aeronautics and Astronautics, University of Tokyo
3 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion
4 Meisei University

Dynamic mode decomposition (DMD), based on Koopman analysis, is a tool capable of spatiotemporal analysis for various spatial resolutions, from one-dimensional signals to three-dimensional computational fluid dynamics (CFD) and experimental data. Outputs of the DMD consist of amplitudes, frequencies, decaying rates, and spatial modes. However, the effects of spatial resolution (time-series data in one-dimensional signal and spatial grid in two-dimensional data) and quantitative analysis of DMD are limited to one-dimensional signal data. In this study, the effects of spatial resolution with a fixed time scale of data and correction using scaling factors 2/sqrt(A) on DMD amplitudes and sqrt(A) on DMD spatial mode strengths are investigated, where A is the number of the time-series data in one-dimensional signal or the number of the spatial grid in two-dimensional data. First, proofs of the scaling factors for one-dimensional(line layout) and two-dimensional(grid layout) data are presented. Second, the effect of spatial resolution on the amplitudes and spatial mode strengths and their scaled results are confirmed using one-dimensional artificial signal data, two-dimensional artificial signal field data, two-dimensional vortex shedding simulation data, and two-dimensional pulsating flow experimental data with various data resolutions. The results show that the amplitude increases proportionally with the spatial resolution, and the spatial mode strength is inversely proportional to the time series or spatial resolution of the data in all cases. As a result of applying the scaling factors to one-dimensional artificial signal and two-dimensional artificial signal field data, the amplitudes and spatial modes contain the same values regardless of the change in spatial resolutions. The scaled amplitudes and spatial mode strengths on vortex shedding simulation and two-dimensional laminar pulsating jet show good agreements with slight differences, regardless of the spatial resolution change. The proposed scaling factor can be applied to compare data quantitatively obtained with different spatial resolutions.

Mots clés: Dynamic mode decomposition;Spatial resolution;Scaling factor;DMD amplitudes;DMD spatial mode

Domaines: Physique [physics]

Jeonghoon Lee, Laurent Zimmer, Takeshi Saito, Shinji Nakaya, Mitsuhiro Tsue. Effects of spatial resolution of the data on dynamic mode decomposition and its quantitative analysis. Experimental Thermal and Fluid Science, 2023, pp.111077. ⟨10.1016/j.expthermflusci.2023.111077⟩. ⟨hal-04268702⟩