Four-Sided Lid-Driven Cavity Flow using Time Splitting Method of Adams-Bashforth Scheme

Azwadi, C. S. Nor; Rajab, Azizah; Sofianuddin, A.S. Ahmad

doi:10.15282/ijame.9.2014.2.0124

Cited by 7 publications

(9 citation statements)

References 23 publications

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“…We have compared the locations of vortices which occur in the vicinity of four walls in Table 2. It is found that our results and those of [9,10], are in good agreement.…”

Section: Code Validationsupporting

confidence: 85%

“…11 and 12). Also, to determine the accuracy of our present numerical scheme, we have studied the four-sided, lid-driven square cavity problem investigated by Perumal and Dass [9], and Azwadi et al [10]. We have compared the locations of vortices which occur in the vicinity of four walls in Table 2.…”

Section: Code Validationmentioning

confidence: 99%

“…Wabha has found that the flow field bifurcates from a stable symmetric state to a stable asymmetric state at critical Reynolds numbers 1073 and 129 for a two-sided and four-sided lid driven cavity respectively. Perumal and Dass [8,9] and Azwadi et al [10] have investigated the steady state solutions of two-dimensional, two-and four-sided lid driven cavity flows in a square cavity using the Lattice Boltzmann Method, the FAS Multigrid method and a time splitting method of the Adams-Bashforth scheme respectively at low Reynolds numbers. Sivasankaran et al [11] have numerically studied the heat and mass transfer in a top side lid-driven square cavity with sinusoidal heating on its vertical walls.…”

Section: Introductionmentioning

confidence: 99%

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The four-sided lid driven square cavity using stream function-vorticity formulation

Bagai¹,

Kumar²,

Patel³

2020

J. Appl. Math. Comput. Mech.

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In this paper, an unsteady 2-D incompressible fluid flow with heat and mass transfer in a four-sided lid driven square cavity is investigated numerically. The top, bottom, left, and right walls of the square cavity move to the right, left, downward and upward respectively. All four sides of the cavity move with a uniform velocity. The flow variables are simulated below the critical Reynolds numbers with isothermal and mass-transfer conditions in the square cavity. We have used a streamfunction-vorticity (ψ − ξ) formulation to investigate the fluid flow in terms of flow variables ψ, ξ , T and C at low Reynolds numbers (Re). The Prandtl number (Pr) and Schmidt number (Sc) have been chosen as 6.62 and 10, 50, 100, 150 respectively, in order to calculate the numerical solutions of T and C. The matrix method has been used to evaluate the stability and convergence of the numerical scheme. The conditions obtained from the matrix method have been used to arrive at the numerical solutions with desired accuracy.

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“…We have compared the locations of vortices which occur in the vicinity of four walls in Table 2. It is found that our results and those of [9,10], are in good agreement.…”

Section: Code Validationsupporting

confidence: 85%

Section: Code Validationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The four-sided lid driven square cavity using stream function-vorticity formulation

Bagai¹,

Kumar²,

Patel³

2020

J. Appl. Math. Comput. Mech.

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“…The geometric simplicity of the problem makes it ideal for numerical discretization and computations, while the discontinuous mathematical boundary condition for the velocity leads to singular properties close to the corners of the moving lid at the two neighboring stationary walls. Azwadi et al (2014) studied the cavity flow for four-sided square lid-driven cavity flow by using a second-order Adams-Bashforth method. They simulated the flow at below critical Reynolds numbers in a square cavity with an isothermal condition and the same speed for all walls.…”

Section: Introductionmentioning

confidence: 99%

Combined effects of the velocity and the aspect ratios on the bifurcation phenomena in a two-sided lid-driven cavity flow

Hammami

Ben–Cheikh

Ben-Beya

et al. 2018

HFF

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Purpose This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0). Design/methodology/approach The numerical method is based on the FVM and multigrid acceleration. Findings Computations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories. Originality/value The bifurcations between steady and unsteady states are investigated.

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“…They have obtained the numerical solutions for the flow variables as well as local and average Nusselt numbers (to analyze the heat transfer inside the cavity) using the QUICK scheme of finite volume methods. Azwadi et al [3] have used the Adams-Bashforth method to investigate the fluid flow inside a four-sided lid-driven square cavity, at below the critical Reynolds numbers (Re ≤ 127) . Bagai et al [4] have examined the problem of heat and mass transfer of a 2-D unsteady incompressible fluid flow in a four-sided lid-driven square cavity with the help of stream functionvorticity formulation and ADI method.…”

Section: Introductionmentioning

confidence: 99%

Mixed convection in four-sided lid-driven sinusoidally heated porous cavity using stream function-vorticity formulation

2020

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This study presents the mixed convection inside a four-sided lid-driven square porous cavity whose right wall is maintained at a sinusoidal temperature condition, the left wall of the cavity is maintained at a cold temperature, while the top and the bottom walls are adiabatic. We have discussed two different cases depending upon the direction of the moving walls. Brinkmann-extended Darcy model is represented in terms of and using the stream function-vorticity formulation to simulate the momentum transfer in the porous medium. This formulation is used to solve the governing equations as a coupled system of equations which consists of the field variables, vorticity () , stream function () , and temperature (T). The velocity components (u, v) are derived from the stream function () whereas the average Nusselt number is derived from temperature. The stability and consistency of the applied numerical scheme to the considered problem has been proven by matrix method. The numerical results are investigated by ranging the various dimensionless numbers such as Grashof number (10 3 ≤ Gr ≤ 10 5) , Darcy number (10 −1 ≤ Da ≤ 10 −5) , Reynolds number (10 ≤ Re ≤ 1000) and keeping the Prandtl number (Pr = 0.7) fixed.

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Four-Sided Lid-Driven Cavity Flow using Time Splitting Method of Adams-Bashforth Scheme

Cited by 7 publications

References 23 publications

The four-sided lid driven square cavity using stream function-vorticity formulation

The four-sided lid driven square cavity using stream function-vorticity formulation

Combined effects of the velocity and the aspect ratios on the bifurcation phenomena in a two-sided lid-driven cavity flow

Mixed convection in four-sided lid-driven sinusoidally heated porous cavity using stream function-vorticity formulation

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