Prediction on steady-oscillatory transition via Hopf bifurcation in a three-dimensional (3D) lid-driven cube

Zhang, Jingkui; Cui, Miao; Zuo, Zongliang; Luo, Siyi; Guo, Jianxiang; Qiu, Zhongzhu

doi:10.1016/j.compfluid.2021.105068

Cited by 8 publications

(4 citation statements)

References 52 publications

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“…Besides, bifurcation analysis has been also the subject of some works of References 24‐30,34,35. Rammane et al 10 presented a best meshless algorithm to study the incompressible fluid flow in three different geometries.…”

Section: Motivation and Related Workmentioning

confidence: 99%

“…The first studies conducted on fluid flow consist on two‐dimensional lid‐driven cavity and rectangular cavities. These studies are devoted to the analysis of velocities and pressure fields and flow instabilities by investigating static 11,23‐25 and Hopf bifurcations 13,26,27 . The investigation of the instability is performed also on the symmetric sudden expansion flow experimentally and numerically.…”

Section: Introductionmentioning

confidence: 99%

“…These studies are devoted to the analysis of velocities and pressure fields and flow instabilities by investigating static 11,[23][24][25] and Hopf bifurcations. 13,26,27 The investigation of the instability is performed also on the symmetric sudden expansion flow experimentally and numerically. These investigations lead to the stationary bifurcation due to change of flow profile symmetry according to the critical Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

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Efficient resolution of incompressible Navier–Stokes equations using a robust high‐order pseudo‐spectral approach

Drissi,

Mesmoudi,

Mansouri

2023

Numerical Methods in Fluids

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An accurate numerical tool is presented in this work to investigate the stationary incompressible Navier–Stokes equations. The proposed approach is based on a pseudo‐spectral method for discretizing the differential equations and the asymptotic numerical method to convert nonlinear systems into linear algebraic equations. The coupling of the spectral method with the asymptotic numerical method is considered as an efficient algorithm to solve any nonlinear differential equations. Their efficiency and robustness are examined here on the flow fluid in different canal with different geometries. These computational efficiency and performance have been analysed via several numerical and benchmark examples of incompressible fluid flow in lid‐driven cavity and vortex shedding over L‐Shaped cavity and fluid flow around a square obstacle. The validation of the proposed approach is made by comparison between the obtained results and those calculated using a finite element method or Ansys commercial code. This validation asserts that the presented numerical tool can be promise for solving fluid flow problems with high accuracy.

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Section: Motivation and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient resolution of incompressible Navier–Stokes equations using a robust high‐order pseudo‐spectral approach

Drissi,

Mesmoudi,

Mansouri

2023

Numerical Methods in Fluids

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“…The physics and dynamics behind many fluid dynamics phenomena such as eddies, secondary flows, chaotic particle motions, instabilities, transition and turbulence can be explained by analysing the LDC flow and hence is canonical. The appearance and structure of the large primary eddy and the secondary eddies have been investigated for a wide range of Reynolds numbers, Re and the spanto-width aspect ratio, Γ L , of the cavity [29,30,[32][33][34][35][36][37][38][39]. Here, the Reynolds number is defined using the velocity of the moving lid, U 0 , and the width of the square face of the cavity, L, as Re = U 0 L/ν.…”

Section: Introductionmentioning

confidence: 99%

Near-wall vortical structures in domains with and without curved surfaces

Sharma

Nair

Vishnu

et al. 2023

Phil. Trans. R. Soc. A.

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Taylor–Couette flow is a canonical flow to study Taylor–Görtler (TG) instability or centrifugal instability and the associated vortices. TG instability has been traditionally associated with flow over curved surfaces or geometries. In the computational study, we confirm the presence of TG-like near-wall vortical structures in two lid-driven flow systems, the Vogel–Escudier (VE) and the lid-driven cavity (LDC) flows. The VE flow is generated inside a circular cylinder by a rotating lid (top lid in the present study), while the LDC flow is generated inside a square or rectangular cavity by the linear movement of the lid. We look at the emergence of these vortical structures through reconstructed phase space diagrams and find that the TG-like vortices are seen in the chaotic regimes in both flows. In the VE flow, these vortices are seen when the side-wall boundary layer instability sets in at large R e . The VE flow is observed to go to a chaotic state in a sequence of events from a steady state at low R e . In contrast to VE flows, in the LDC flow with no curved boundaries, TG-like vortices are seen at the emergence of unsteadiness when the flow exhibits a limit cycle. The LDC flow is observed to have transitioned to chaos from the steady state through a periodic oscillatory state. Various aspect ratio cavities are examined in both flows for the presence of TG-like vortices. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical transactions paper (Part 2)’.

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Non-relaxed finite volume fractional step schemes for unsteady incompressible flows

Díaz

Castillo

Cabrales

et al. 2023

Computers & Mathematics with Applications

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Prediction on steady-oscillatory transition via Hopf bifurcation in a three-dimensional (3D) lid-driven cube

Cited by 8 publications

References 52 publications

Efficient resolution of incompressible Navier–Stokes equations using a robust high‐order pseudo‐spectral approach

Efficient resolution of incompressible Navier–Stokes equations using a robust high‐order pseudo‐spectral approach

Near-wall vortical structures in domains with and without curved surfaces

Non-relaxed finite volume fractional step schemes for unsteady incompressible flows

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