Transition to complex dynamics in the cubic lid-driven cavity

Lopez, Juan M.; Welfert, Bruno D.; Wu, Ke; Yalim, Jason

doi:10.1103/physrevfluids.2.074401

Cited by 24 publications

(47 citation statements)

References 23 publications

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“…The reason for this can be the subcritical type of this bifurcation, as was argued in [10,14,15]. [14,16,18], are close to one reported here. Note, that all the three studies report an unstable limit cycle in the slightly supercritical regime.…”

Section: Critical Parameters Of the Lid-driven Flow In A Cubesupporting

confidence: 90%

“…Unfortunately, none of the papers where the steady states and the eigenvalues were computed directly, e.g., [14,[16][17][18], did report consumed computational times, so that a direct comparison is impossible. The characteristic times for computation of the steady states were 400 -600 sec for the 100 3 grid and 5 -10 hours for the 256 3 grid.…”

Section: Correctmentioning

confidence: 99%

“…Note, that all the three studies report an unstable limit cycle in the slightly supercritical regime. It is worth to mention that the cyclic-fold bifurcation between the upper and lower branches of the subcritical limit cycle was calculated in [18] to be located at ≈ 1913.5, which is close to the value 1914, which is the Richardson extrapolation of the Reynolds numbers corresponding to the appearance of subcritical oscillations at different grids in the time-dependent calculations of [10]. At the same time the three studies [10-12] report qualitatively different supercritical flow states.…”

Section: Critical Parameters Of the Lid-driven Flow In A Cubementioning

confidence: 99%

“…In several other studies [16,17], the leading eigenvalues were computed to determine whether the flow is stable or unstable, however no attempt to arrive at an accurate value of the critical Reynolds number was made. The first thorough linear stability analysis was performed only recently in [18].…”

Section: Introductionmentioning

confidence: 99%

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Linear instability of the lid-driven flow in a cubic cavity

Gelfgat

2019

Theor. Comput. Fluid Dyn.

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Primary instability of the lid-driven flow in a cube is studied by a linear stability approach.Two cases, in which the lid moves parallel to the cube sidewall or parallel to the diagonal plane, are considered. It is shown that Krylov vectors required for application of the Newton and Arnoldi iteration methods can be evaluated by the SIMPLE procedure. The finite volume grid is gradually refined from 100 3 to 256 3 nodes. The computations result in grid converging values of the critical Reynolds number and oscillation frequency that allow for Richardson extrapolation to the zero grid size. Three-dimensional flow and most unstable perturbations are visualized by a recently proposed approach that allows for a better insight in the flow patterns and appearance of the instability. New arguments regarding the assumption that the centrifugal mechanism triggers the instability are given for both cases.Keywords: lid-driven cavity flow, Newton method, Arnoldi method, linear stability, Krylovsubspace iteration, SIMPLE steady-oscillatory transition was studied recently in [22], again by the straightforward integration in time.Our primary goal is to apply the eigenvalue analysis for calculation of the critical Reynolds numbers, at which the steady flow bifurcates to an oscillatory state. The computations are carried out using gradually refined stretched grids, containing 100 3 , 150 3 , 200 3 , and 256 3 finite volumes. In spite that pseudo-spectral and collocation methods may yield better accuracy for model problems in simple geometries, as those considered here, they are not applicable to most of the applied problems that involve more complicated flow regions and liquid-liquid interfaces. Besides a wide set of curved-boundary-fitted numerical methods, such problems can be treated by the fixed grid finite volume approach used below with the immersed boundary technique, as it was done recently in [23].The critical Reynolds numbers are calculated together with the critical oscillation frequencies. These are defined by the imaginary part of the leading eigenvalue, whose real part crosses the imaginary axis at the stability limit. The most unstable infinitesimally small perturbation is defined by the eigenvector corresponding to the leading eigenvalue. The eigenvector spatial pattern allows us to compare with the results of previous studies that applied the straightforward integration in time, to visualize spatio-temporal behavior of the most unstable disturbance, and basing on this to speculate further about the reasons that cause the instability onset.In the following we formulate the problem and briefly describe the numerical method, as well as our method of visualization of three-dimensional divergence-free velocity field [24,25]. The present numerical approach includes Newton iteration for calculation of the steady states and Arnoldi iteration for computation of leading eigenvalues. The Newton corrections are computed by the Krylov-subspace-iteration techniques BiCGstab(2) or GMRES. The SIMPLE procedure [26] is reformulated ...

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Section: Critical Parameters Of the Lid-driven Flow In A Cubesupporting

confidence: 90%

Section: Correctmentioning

confidence: 99%

Section: Critical Parameters Of the Lid-driven Flow In A Cubementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Linear instability of the lid-driven flow in a cubic cavity

Gelfgat

2019

Theor. Comput. Fluid Dyn.

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“…This leads to an intermittent chaotic behavior with periods of symmetric and asymmetric oscillations [3,5]. However, the bifurcation scenario is different: In the LDC the basic flow becomes linearly unstable at Re LDC = 1921 [3] to a backward-bifurcating oscillatory but symmetric mode.…”

Section: Discussionmentioning

confidence: 99%

Three‐dimensional flow in a shear‐driven cube

Boscs

Kuhlmann

2019

Proc Appl Math and Mech

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The flow in a cubic cavity is studied when a constant shear stress is imposed on one of its square faces. The three-dimensional basic flow undergoes a first steady, symmetry-breaking, pitchfork bifurcation. On an increase of the Reynolds number the symmetry-broken flow becomes time-dependent via a Hopf bifurcation. Even though the basic flow is similar to the one in the lid-driven cube, the sequence of bifurcations differs significantly.

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The Lid-Driven Cavity

Kuhlmann

Romanò

2018

Computational Methods in Applied Sciences

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Transition to complex dynamics in the cubic lid-driven cavity

Cited by 24 publications

References 23 publications

Linear instability of the lid-driven flow in a cubic cavity

Linear instability of the lid-driven flow in a cubic cavity

Three‐dimensional flow in a shear‐driven cube

The Lid-Driven Cavity

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