A parallel and streaming Dynamic Mode Decomposition algorithm with finite precision error analysis for large data

Anantharamu, Sreevatsa; Mahesh, Krishnan

doi:10.1016/j.jcp.2018.12.012

Cited by 16 publications

(11 citation statements)

References 25 publications

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“…DMD is a useful tool to isolate the regions associated with a particular frequency and provide information on system dynamics. For the present work, we use a novel DMD algorithm developed by Anantharamu & Mahesh (2019) that is suitable for analysis of large datasets. The basic idea behind DMD is that the set of snapshot vectors of flow variables can be written as a linear combination of DMD modes as where are the eigenvalues of the projected linear mapping and are the th entries of the first vector .…”

Section: Resultsmentioning

confidence: 99%

Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Mahesh

2022

J. Fluid Mech.

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Global stability analysis and direct numerical simulation (DNS) are used to study boundary layer flows with an isolated roughness element. The aspect ratio of the element ( $\eta$ ) is small, while the ratio of element height to displacement boundary layer thickness ( $h/\delta ^{*}$ ) is large. Both steady base flows and time-averaged mean flows are able to capture the frequencies of the primary vortical structures and mode shapes. Global stability results highlight that although the varicose instability is dominant for large $h/\delta ^{*}$ , sinuous instability becomes more pronounced as $Re_h$ increases for the thin geometry ( $\eta =0.5$ ), due to increased spanwise shear in the near-wake region. Wavemaker results indicate that $\eta$ affects the convective nature of the shear layer more than the type of instability. DNS results show that different instability mechanisms lead to different development and evolution of vortical structures in the transition process. For $\eta =1$ , the varicose instability is associated with the periodic shedding of hairpin vortices, and its stronger spatial transient growth indicated by wavemaker results aids the formation of hairpin vortices farther downstream. In contrast, for $\eta =0.5$ , the interplay between varicose and sinuous instabilities results in a broader-banded energy spectrum and leads to the sinuous wiggling of hairpin vortices in the near wake when $Re_h$ is sufficiently high. A sinuous mode with a lower frequency captured by dynamic mode decomposition analysis, and associated with the ‘wiggling’ of streaks, persists far downstream and promotes transition to turbulence. A new regime map is developed to classify and predict instability mechanisms based on $Re_{hh}^{1/2}$ and $d/\delta ^{*}$ using a logistic regression model. Although the mean skin friction demonstrates different evolutions for the two geometries, both of them efficiently trip the flow to turbulence at $Re_h=1100$ . An earlier location of a fully-developed turbulent state is established for $\eta =1$ at $x \approx 110h$ .

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Section: Resultsmentioning

confidence: 99%

Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Mahesh

2022

J. Fluid Mech.

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“…The obtained modes and their eigenvalues capture the system dynamics. We use a novel DMD algorithm developed by Anantharamu & Mahesh (2019) that has low computational cost and low memory requirements. The basic idea behind DMD is that the set of observable vectors (snapshot vectors of flow variables) {ψ i } N −1 i=1 can be written as a linear combination of DMD modes {φ i } N −1 i=1 as…”

Section: Dynamic Mode Decompositionmentioning

confidence: 99%

“…where λ j are the eigenvalues of the projected linear mapping and c j are the j th entry of the first vector ψ 1 . The complete derivation of the algorithm can be seen in Anantharamu & Mahesh (2019). For the cyclic and non-cavitating regime around N = 200 snapshots of the flow field were taken with ∆t/(D/u ∞ ) = 0.1 between them, while N = 400 snapshots with ∆t/(D/u ∞ ) = 0.5 were taken for the transitional regimes.…”

Section: Dynamic Mode Decompositionmentioning

confidence: 99%

Numerical study of cavitation regimes in flow over a circular cylinder

2019

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Cavitating flow over a circular cylinder is investigated over a range of cavitation numbers (σ = 5 to 0.5) for both laminar (at Re = 200) and turbulent (at Re = 3900) regimes. We observe non-cavitating, cyclic and transitional cavitation regimes with reduction in freestream σ. The cavitation inside the Kármán vortices in the cyclic regime, is significantly altered by the onset of "condensation front" propagation in the transitional regime. At the transition, an order of magnitude jump in shedding Strouhal number is observed as the dominant frequency shifts from periodic vortex shedding in the cyclic regime, to irregular-regular vortex shedding in the transitional regime. In addition, a peak in pressure fluctuations, and a maximum in St versus σ based on cavity length are observed at the transition. Shedding characteristics in each regime are discussed using dynamic mode decomposition (DMD). A numerical method based on the homogeneous mixture model, fully compressible formulation and finite rate mass transfer developed by Gnanaskadan & Mahesh (Intl. J. Multiphase Flows, vol. 70, 2015, pp. 22-34) is extended to include the effects of non-condensable gas (NCG). It is demonstrated that the condensation fronts observed in the transitional regime are supersonic (referred as "condensation shocks"). In the presence of NCG, multiple condensation shocks in a given cycle are required for complete cavity condensation and detachment, as compared to a single condensation shock when only vapor is present. This is explained by the reduction in pressure ratio across the shock in the presence of NCG effectively reducing its strength. In addition, at σ = 0.85 (near transition from the cyclic to the transitional regime), presence of NCG suppresses the low frequency irregular-regular vortex shedding. Vorticity transport at Re = 3900, in the transitional regime, indicates that the region of attached cavity is nearly two-dimensional with very low vorticity, affecting Kármán shedding in the near wake. Majority of vortex stretching/tilting and vorticity production is observed following the cavity trailing edge. In addition, the boundary-layer separation point is found to be strongly dependent on the amounts of vapor and gas in the freestream for both laminar and turbulent regimes. 1 2 ρ∞U 2 ∞ , where p ∞ , ρ ∞ and U ∞ are pressure, density and velocity in the freestream respectively) in the freestream is sufficiently dropped, cavities develop †

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“…Before applying sDMD to the three aforementioned datasets, we first compare classical and streaming DMD implementations in terms of their respective memory consumption for a publicly available dataset [31] that has been extensively used for testing and validation purposes in the literature [2,9]. Subsequently, we use this dataset to test DMD in conjunction with a coarsening interpolation scheme designed to reduce the computational effort when analyzing data of high spatial dimension M, as will be the case for turbulent flows.…”

Section: Validationmentioning

confidence: 99%

“…Therefore, only a few studies so far have applied DMD to highly turbulent flows. These constraints can be circumvented by a DMD implementation that allows for incremental data updates [2,19,63], such that the DMD calculation proceeds alongside the main data acquisition process such as Direct Numerical Simulations (DNS) or real-time Particle Image Velocimetry. Streaming DMD (sDMD) [19] is such a method, which requires only two data samples at a given instant in time and converges to the same results as classical DMD. In what follows we focus on sDMD as a promising method for the analysis of turbulent flows.…”

Section: Introductionmentioning

confidence: 99%

Data‐driven identification of the spatiotemporal structure of turbulent flows by streaming dynamic mode decomposition

et al. 2022

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Streaming Dynamic Mode Decomposition (sDMD) is a low‐storage version of dynamic mode decomposition (DMD), a data‐driven method to extract spatiotemporal flow patterns. Streaming DMD avoids storing the entire data sequence in memory by approximating the dynamic modes through incremental updates with new available data. In this paper, we use sDMD to identify and extract dominant spatiotemporal structures of different turbulent flows, requiring the analysis of large datasets. First, the efficiency and accuracy of sDMD are compared to the classical DMD, using a publicly available test dataset that consists of velocity field snapshots obtained by direct numerical simulation of a wake flow behind a cylinder. Streaming DMD not only reliably reproduces the most important dynamical features of the flow; our calculations also highlight its advantage in terms of the required computational resources. We subsequently use sDMD to analyse three different turbulent flows that all show some degree of large‐scale coherence: rapidly rotating Rayleigh–Bénard convection, horizontal convection and the asymptotic suction boundary layer (ASBL). Structures of different frequencies and spatial extent can be clearly separated, and the prominent features of the dynamics are captured with just a few dynamic modes. In summary, we demonstrate that sDMD is a powerful tool for the identification of spatiotemporal structures in a wide range of turbulent flows.

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A parallel and streaming Dynamic Mode Decomposition algorithm with finite precision error analysis for large data

Cited by 16 publications

References 25 publications

Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Numerical study of cavitation regimes in flow over a circular cylinder

Data‐driven identification of the spatiotemporal structure of turbulent flows by streaming dynamic mode decomposition

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