Transition in a 2-D lid-driven cavity flow

Peng, Yih‐Ferng; Shiau, Yuo-Hsien; Hwang, Robert R.

doi:10.1016/s0045-7930(01)00053-6

Cited by 132 publications

(111 citation statements)

References 28 publications

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“…Peng, Shiau & Hwang [32] have used a Direct Numerical Simulation (DNS) by solving the 2-D unsteady Navier-Stokes equations in primitive variables. With using a maximum of 200×200 grids, they have solved the cavity flow by increasing the Reynolds number.…”

Section: Discussion On Driven Cavity Flowmentioning

confidence: 99%

“…For a moment, let us imagine that the 2-D incompressible flow inside a cavity is not stable at a given Reynolds number, such that a steady solution does not exist and the solution is time dependent, as predicted by [4,32,44,34,10,24,46,31]. In this case, if one uses the steady N-S equations then he should not obtain a solution since there is no steady state solution.…”

Section: Discussion On Driven Cavity Flowmentioning

confidence: 99%

“…In the third category, the following two dimensional Direct Numerical Simulation studies on driven cavity flow, Auteri, Parolini & Quartepelle [4], Peng, Shiau & Hwang [32], Tiesinga, Wubs & Veldman [44], Poliashenko & Aidun [34], Cazemier, Verstappen & Veldman [10], Goyon [24], Wan, Zhou & Wei [46] and Liffman [31] can be found in the literature as an example.…”

Section: Introductionmentioning

confidence: 99%

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Discussions on driven cavity flow

Ertürk

2008

Numerical Methods in Fluids

149

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SUMMARYThe widely studied benchmark problem, 2-D driven cavity flow problem is discussed in details in terms of physical and mathematical and also numerical aspects. A very brief literature survey on studies on the driven cavity flow is given. Based on the several numerical and experimental studies, the fact of the matter is, above moderate Reynolds numbers physically the flow in a driven cavity is not twodimensional. However there exist numerical solutions for 2-D driven cavity flow at high Reynolds numbers.

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Section: Discussion On Driven Cavity Flowmentioning

confidence: 99%

Section: Discussion On Driven Cavity Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discussions on driven cavity flow

Ertürk

2008

Numerical Methods in Fluids

149

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“…It consists of a square closed cavity of size L whose lid slides laterally at a constant velocity, driving the fluid under the effect of the viscosity. For Reynolds numbers lower than about 7500 [36], it reaches a steady-state after some time. Then, it is possible to compare the results between different computational fluid dynamics (CFD) codes.…”

Section: Lid-driven Cavitymentioning

confidence: 98%

Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH

Leroy

Violeau

Ferrand³

et al. 2014

Journal of Computational Physics

102

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This work aims at improving the 2-D incompressible SPH model (ISPH) by adapting it to the unified semi-analytical wall boundary conditions proposed by Ferrand et al. [10]. The ISPH algorithm considered is as proposed by Lind et al. [25], based on the projection method with a divergence-free velocity field and using a stabilising procedure based on particle shifting. However, we consider an extension of this model to Reynolds-Averaged Navier-Stokes equations based on the k − ǫ turbulent closure model, as done in [10]. The discrete SPH operators are modified by the new description of the wall boundary conditions. In particular, a boundary term appears in the Laplacian operator, which makes it possible to accurately impose a von Neumann pressure wall boundary condition that corresponds to impermeability. The shifting and free-surface detection algorithms have also been adapted to the new boundary conditions. Moreover, a new way to compute the wall renormalisation factor in the frame of the unified semi-analytical boundary conditions is proposed in order to decrease the computational time. We present several verifications to the present approach, including a lid-driven cavity, a water column collapsing on a wedge and a periodic schematic fish-pass. Our results are compared to Finite Volumes methods, using Volume of Fluids in the case of free-surface flows. We briefly investigate the convergence of the method and prove its ability to model complex free-surface and turbulent flows. The results are generally improved when compared to a weakly compressible SPH model with the same boundary conditions, especially * Corresponding author. tel: +33 (0)6 67 88 92 13Email addresses: agnes.leroy@edf.fr (A. Leroy), damien.violeau@edf.fr (D. Violeau),

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“…Many scholars [1][2][3][4][5][6][7][8][9][10][11][12] dedicated themselves into this field. In 1982, Giha et al [1] studied two dimensional lid driven square cavity flow by solving the Navier-Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of the 2D Lid-driven Triangular Cavities Based on the Lattice Boltzmann Method

An¹,

Bergad...²

2017

Proceedings of the 3rd Annual International Conference on Mechanics and Mechanical Engineering (MME 2016)

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Keywords: Lattice Boltzmann method, Triangular cavity, Steady and unsteady flow.Abstract. Numerical study of two dimensional lid driven triangular cavity flow is performed via using lattice Boltzmann method on low Reynolds numbers. The equilateral triangular cavity is the first geometry to be studied, the simulation is performed at Reynolds number 500 and the numerical prediction is compared with previous work done by other scholars. Several isosceles triangular cavities are studied at different initial conditions, Reynolds numbers ranging from 100 to 3000, regardless of the geometry studied, the top lid is always moving from left to right and the driven velocity remains constant. Results are also compared with previous work performed by other scholars, the agreement is very good. According to the authors' knowledge, this is the first time that MRT-LBM model is used to simulate the flow inside the triangular cavities. One of the advantages of this method is that it is capable of producing at low and high Reynolds numbers.

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Transition in a 2-D lid-driven cavity flow

Cited by 132 publications

References 28 publications

Discussions on driven cavity flow

Discussions on driven cavity flow

Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH

Numerical Study of the 2D Lid-driven Triangular Cavities Based on the Lattice Boltzmann Method

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