Multiple Hopf bifurcations and flow dynamics inside a 2D singular lid driven cavity

Lestandi, Lucas; Bhaumik, Swagata; Avatar, G.R.K.C.; Azaïez, Mejdi; Sengupta, Tapan K.

doi:10.1016/j.compfluid.2018.01.038

Cited by 18 publications

(18 citation statements)

References 41 publications

(137 reference statements)

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“…Poliashenko and Aidun [26] on the other hand reported a value of Re cr1 = 7763±2% using a commercial FEM package. Using the present method [41] with a (257×257) grid, a value of Re cr1 ≈ 8665 has been reported by Lestandi et al [22], for the case of no explicit excitation applied. A major difference is that computations for all the cases presented here have been performed following an impulsive start.…”

Section: Introductionsupporting

confidence: 56%

“…For the refined grid, onset of unsteadiness occurs for Re slightly lower than 9450, for the case of A 0 = 0. The (257×257) grid results also show a dip in A e around Re = 9400, which is identified as the second bifurcation point [22] for this grid. In this reference, different bifurcation sequences are identified by plotting A 2 e versus Re and the segments are identified by straight lines with different slope for the unexcited cases.…”

Section: Flow Dynamics In Ldc: Bifurcation Sequencesmentioning

confidence: 59%

“…All computations are performed with non-dimensional time-step of ∆t = 10 −3 . Additional details of the method for this problem is in [22], which explained the reason for the location where time-series for vorticity is stored for analysis. This is shown in Figure 1(a) as P, with the coordinate (x = 0.95,y = 0.95).…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…Impulsive start of the flow triggers all frequencies at the onset and hence preferred [38,42]. Obtaining final limit cycle at one Re from the limit cycle solution from another Re [25] is inappropriate [22]. First Hopf bifurcation obtained by DNS is dependent upon source of numerical error, mainly on the aliasing error for flow inside LDC [42].…”

Section: Introductionmentioning

confidence: 99%

“…The point located at (x = 0.95,y = 0.95) is used here for sampling the data, which is very close to the singularity at the top right corner, and will log larger value of disturbances [22,41,42]. A recent study [22] highlights aspects of computing flow inside LDC based on study of time series at this point. Although, it is a valid way of studying the flow dynamics in LDC, it is desirable to use a global flow analysis tool like POD, which provides spatio-temporal information for the full domain.…”

Section: Introductionmentioning

confidence: 99%

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POD Applied to Numerical Study of Unsteady Flow Inside Lid-driven Cavity

Lestandi¹

2018

JMS

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Flow inside a lid-driven cavity (LDC) is studied here to elucidate bifurcation sequences of the flow at super-critical Reynolds numbers (Re cr1 ) with the help of analyzing the time series at most energetic points in the flow domain. The implication of Re cr1 in the context of direct simulation of Navier-Stokes equation is presented here for LDC, with or without explicit excitation inside the LDC. This is aided further by performing detailed enstrophy-based proper orthogonal decomposition (POD) of the flow field. The flow has been computed by an accurate numerical method for two different uniform grids. POD of results of these two grids help us understand the receptivity aspects of the flow field, which give rise to the computed bifurcation sequences by understanding the similarity and differences of these two sets of computations. We show that POD modes help one understand the primary and secondary instabilities noted during the bifurcation sequences.

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Section: Introductionsupporting

confidence: 56%

Section: Flow Dynamics In Ldc: Bifurcation Sequencesmentioning

confidence: 59%

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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POD Applied to Numerical Study of Unsteady Flow Inside Lid-driven Cavity

Lestandi¹

2018

JMS

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New compact difference schemes on non‐uniform collocated and staggered grids for convection‐dominated flows

Yadav

Maurya²,

Rajpoot

2022

Numerical Methods in Fluids

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Summary This paper deals with the formulation of the tridiagonal compact difference schemes for derivatives up to second‐order with boundary stencils on non‐uniform grids. A compact scheme for the first derivative with interpolation is also devised on staggered non‐uniform grids. The developed schemes with non‐uniform spacing transform to respective classical compact schemes for the case of uniform mesh spacing. The resolution, numerical diffusion, and anti‐diffusion features of the devised schemes are evaluated using global spectral analysis. Applications to the direct numerical simulation (DNS) of two‐dimensional lid‐driven cavity (LDC) flow governed by Navier‐Stokes equations and wave‐propagation following linear rotating shallow water (LRSWE) equations with variable grid‐spacing are discussed at different choices of parameters. Computed results are also compared with solutions available in the literature.

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Numerical Study of Low Rank Approximation Methods for Mechanics Data and Its Analysis

Lestandi

2021

J Sci Comput

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Multiple Hopf bifurcations and flow dynamics inside a 2D singular lid driven cavity

Cited by 18 publications

References 41 publications

POD Applied to Numerical Study of Unsteady Flow Inside Lid-driven Cavity

POD Applied to Numerical Study of Unsteady Flow Inside Lid-driven Cavity

New compact difference schemes on non‐uniform collocated and staggered grids for convection‐dominated flows

Numerical Study of Low Rank Approximation Methods for Mechanics Data and Its Analysis

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