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Journal articles on the topic 'Lid-Driven-Cavity Flow'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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1

Kumar, Jitendra, and N. R. Panchapakesan. "Numerical Investigation of Rotating Lid-driven Cubical Cavity Flow." Defence Science Journal 67, no. 3 (April 25, 2017): 233. http://dx.doi.org/10.14429/dsj.67.10289.

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<p>The present work numerically investigates the flow field in a cubical cavity driven by a lid rotating about an axis passing through its geometric center. Behaviour of core flow and secondary vortical structures are presented. Grid-free critical Reynolds number at which flow turns oscillatory is estimated to be 1606. This differs significantly from the linear lid-driven cubical cavity as well as circular lid-driven cylindrical cavity flows which have been reported to attain unsteadiness at higher Reynolds numbers. A stationary vortex bubble similar to rotating lid-driven cylindrical cavity flow has been observed to be present in the flow.</p>

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2

Sousa, R. G., R. J. Poole, A. M. Afonso, F. T. Pinho, P. J. Oliveira, A. Morozov, and M. A. Alves. "Lid-driven cavity flow of viscoelastic liquids." Journal of Non-Newtonian Fluid Mechanics 234 (August 2016): 129–38. http://dx.doi.org/10.1016/j.jnnfm.2016.03.001.

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3

Ramanan, Natarajan, and George M. Homsy. "Linear stability of lid‐driven cavity flow." Physics of Fluids 6, no. 8 (August 1994): 2690–701. http://dx.doi.org/10.1063/1.868158.

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4

Mužík, Juraj, and Roman Bulko. "Lid-driven cavity flow using dual reciprocity." MATEC Web of Conferences 313 (2020): 00043. http://dx.doi.org/10.1051/matecconf/202031300043.

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The paper presents the use of the multi-domain dual reciprocity method of fundamental solutions (MD-MFSDR) for the analysis of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using the method of fundamental solutions with the 2D Stokes fundamental solution Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the non-homogeneous and nonlinear terms of Navier-Stokes equations. The presented DR-MFS approach to the solution of the 2D flow problem is demonstrated on a standard benchmark problem - lid-driven cavity.

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5

Albensoeder, S., and H. C. Kuhlmann. "Accurate three-dimensional lid-driven cavity flow." Journal of Computational Physics 206, no. 2 (July 2005): 536–58. http://dx.doi.org/10.1016/j.jcp.2004.12.024.

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6

Chen, C. K., and D. T. W. Lin. "TIP4P potential for lid-driven cavity flow." Acta Mechanica 178, no. 3-4 (August 2005): 223–37. http://dx.doi.org/10.1007/s00707-004-0110-5.

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7

Hoang-Trong, Chuong Nguyen, Cuong Mai Bui, and Thinh Xuan Ho. "Lid-driven cavity flow of sediment suspension." European Journal of Mechanics - B/Fluids 85 (January 2021): 312–21. http://dx.doi.org/10.1016/j.euromechflu.2020.10.003.

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8

HAMMAMI, FAYÇAL, NADER BEN-CHEIKH, ANTONIO CAMPO, BRAHIM BEN-BEYA, and TAIEB LILI. "PREDICTION OF UNSTEADY STATES IN LID-DRIVEN CAVITIES FILLED WITH AN INCOMPRESSIBLE VISCOUS FLUID." International Journal of Modern Physics C 23, no. 04 (April 2012): 1250030. http://dx.doi.org/10.1142/s0129183112500301.

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In this work, a numerical study devoted to the two-dimensional and three-dimensional flow of a viscous, incompressible fluid inside a lid-driven cavity is undertaking. All transport equations are solved using the finite volume formulation on a staggered grid system and multi-grid acceleration. Quantitative aspects of two and three-dimensional flows in a lid-driven cavity for Reynolds number Re = 1000 show good agreement with benchmark results. An analysis of the flow evolution demonstrates that, with increments in Re beyond a certain critical value Rec, the steady flow becomes unstable and bifurcates into unsteady flow. It is observed that the transition from steadiness to unsteadiness follows the classical Hopf bifurcation. The time-dependent velocity distribution is studied in detail and the critical Reynolds number is localized for both 2D and 3D cases. Benchmark solutions for 2D and 3D lid-driven cavity flows are performed for Re = 1500 and 6000.

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9

Biswas, Sougata, and Jiten C. Kalita. "Moffatt vortices in the lid-driven cavity flow." Journal of Physics: Conference Series 759 (October 2016): 012081. http://dx.doi.org/10.1088/1742-6596/759/1/012081.

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10

Zhang, Chao, Hui Zhao, Xingzhi Hu, and Jiangtao Chen. "Stochastic Characteristic Analysis of Lid-Driven Cavity Flow." Journal of Physics: Conference Series 1600 (July 2020): 012037. http://dx.doi.org/10.1088/1742-6596/1600/1/012037.

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11

Stremler, Mark A., and Jie Chen. "Generating topological chaos in lid-driven cavity flow." Physics of Fluids 19, no. 10 (October 2007): 103602. http://dx.doi.org/10.1063/1.2772881.

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12

Teixeira, Christopher M. "Digital Physics Simulation of Lid-Driven Cavity Flow." International Journal of Modern Physics C 08, no. 04 (August 1997): 685–96. http://dx.doi.org/10.1142/s0129183197000588.

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Digital Physics is a new extension of the lattice-gas concept for the simulation of fluid flow which removes disadvantages that prevented practical application of the original method. The extensions are summarized. Simulation results for a three-speed model demonstrate the absence of artifacts and significant reduction in viscosity. Also, simulation results for 2D and 3D lid-driven cavities for a range of Reynolds numbers and geometries are compared with experiment, CFD and the lattice-Boltzmann BGK method. Accurate results are obtained with the new method.

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13

Selimefendigil, Fatih, and Ali Jawad Chamkha. "Ferrofluid Convection in a Lid-Driven Cavity." Defect and Diffusion Forum 388 (October 2018): 407–19. http://dx.doi.org/10.4028/www.scientific.net/ddf.388.407.

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This study numerically investigates the mixed convection of ferrofluids in a partially heated lid driven square enclosure. The heater is located to the left vertical wall and the right vertical wall is kept at constant lower temperature while other walls of the cavity are assumed to be adiabatic. The governing equations are solved with Galerkin weighted residual finite element method. The influence of the Richardson number (between 0.01 and 100), heater location (between 0.25 H and 0.75H), strength of the magnetic dipole (between 0 and 4), and horizontal location of the magnetic dipole source (between-2H and-0.5H) on the fluid flow and heat transfer are numerically investigated. It is found that local and averaged heat transfer deteriorates with increasing values of Richardson number and magnetic dipole strength. The flow field and thermal characteristics are sensitive to the magnetic dipole source strength and its position and heater location.

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14

Fazuruddin, Syed, Seelam Sreekanth, and G. Sankara Sekhar Raju. "Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach." Mathematical Modelling of Engineering Problems 8, no. 3 (June 24, 2021): 418–24. http://dx.doi.org/10.18280/mmep.080311.

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Incompressible 2-D Navier-stokes equations for various values of Reynolds number with and without partial slip conditions are studied numerically. The Lid-Driven cavity (LDC) with uniform driven lid problem is employed with vorticity - Stream function (VSF) approach. The uniform mesh grid is used in finite difference approximation for solving the governing Navier-stokes equations and developed MATLAB code. The numerical method is validated with benchmark results. The present work is focused on the analysis of lid driven cavity flow of incompressible fluid with partial slip conditions (imposed on side walls of the cavity). The fluid flow patterns are studied with wide range of Reynolds number and slip parameters.

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15

Perumal, D. Arumuga, and Anoop K. Dass. "Computation of Lattice Kinetic Scheme for Double-Sided Parallel and Antiparallel Wall Motion." Applied Mechanics and Materials 592-594 (July 2014): 1967–71. http://dx.doi.org/10.4028/www.scientific.net/amm.592-594.1967.

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This paper is concerned with the double-sided lid-driven cavity simulation of two-dimensional lattice kinetic scheme on the uniform lattice arrangement based on the standard lattice Boltzmann method. The double-sided lid-driven cavity problem has multiple steady solutions for some aspect ratios. However, for the double-sided square cavity no multiplicity of solutions has been observed for both the parallel and antiparallel motion of the walls. To validate this new lattice kinetic scheme, the numerical simulations of the double-sided square driven cavity flow at Reynolds numbers from 10 to 1000 are carried out. The Reynolds number effect on the flow structure is clearly manifested by the streamline patterns and velocity profiles. It is concluded that the present study in double-sided lid-driven cavity produces results that are in excellent conformity with earlier conventional numerical observations.

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16

Dong, Di Bo, Sheng Jun Shi, Zhen Xiu Hou, and Wei Shan Chen. "Numerical Simulation of Viscous Flow in a 3D Lid-Driven Cavity Using Lattice Boltzmann Method." Applied Mechanics and Materials 444-445 (October 2013): 395–99. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.395.

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A lattice Boltzmann method (LBM) with single-relaxation time and on-site boundary condition is used for the simulation of viscous flow in a three-dimensional (3D) lid-driven cavity. Firstly, this algorithm is validated by compared with the benchmark experiments for a standard cavity, and then the results of a cubic cavity with different inflow angles are presented. Steady results presented are for the inflow angle of and, and the Reynolds number is selected as 500. It is found that for viscous flow under moderate Reynolds number, there exists a primary vortex near the center and a secondly vortex at the lower right corner on each slice when, namely in a standard 3D lid-driven cavity, which cant be found when. So it can be thought that the flow pattern in a 3D lid-driven cavity depends not only on the Reynolds number but also the inflow angle.

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17

Yang, Y., A. G. Straatman, R. J. Martinuzzi, and E. K. Yanful. "A study of laminar flow in low aspect ratio lid-driven cavities." Canadian Journal of Civil Engineering 29, no. 3 (June 1, 2002): 436–47. http://dx.doi.org/10.1139/l02-027.

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The evolution to fully developed laminar flow in low aspect ratio, two-dimensional, lid-driven cavities has been studied experimentally and numerically. Velocity measurements were made in water in a moving-lid apparatus using a laser Doppler velocimeter (LDV). Numerical solutions for the cavity flow were obtained by solving the two-dimensional mass-momentum equation set in a finite-volume framework. The measured and predicted results were in excellent agreement. Fully developed cavity flow is said to exist when the main regions of the flow field become independent of the aspect ratio. When fully developed conditions prevail, a region of countercurrent flow (CCF) separates the end structures, which are decoupled. The extent of the end regions is shown to grow linearly with increasing Reynolds number Re, based on the lid speed and the cavity height. Consequently, the critical aspect ratio for the onset of fully developed flow is also linearly dependent on Re. Above a critical Reynolds number, Re [Formula: see text] 300, the flow becomes unsteady, and a lower-wall, tertiary vortex appears, which is thought to be associated with the onset of hydrodynamic instability.Key words: lid-driven cavity, laminar flow, shallow water cover, countercurrent flow.

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18

An, B., J. M. Bergada, and F. Mellibovsky. "The lid-driven right-angled isosceles triangular cavity flow." Journal of Fluid Mechanics 875 (July 22, 2019): 476–519. http://dx.doi.org/10.1017/jfm.2019.512.

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We employ lattice Boltzmann simulation to numerically investigate the two-dimensional incompressible flow inside a right-angled isosceles triangular enclosure driven by the tangential motion of its hypotenuse. While the base flow, directly evolved from creeping flow at vanishing Reynolds number, remains stationary and stable for flow regimes beyond $Re\gtrsim 13\,400$, chaotic motion is nevertheless observed from as low as $Re\simeq 10\,600$. Chaotic dynamics is shown to arise from the destabilisation, following a variant of the classic Ruelle–Takens route, of a secondary solution branch that emerges at a relatively low $Re\simeq 4908$ and appears to bear no connection to the base state. We analyse the bifurcation sequence that takes the flow from steady to periodic and then quasi-periodic and show that the invariant torus is finally destroyed in a period-doubling cascade of a phase-locked limit cycle. As a result, a strange attractor arises that induces chaotic dynamics.

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19

Grillet, Anne M., Eric S. G. Shaqfeh, and Bamin Khomami. "Observations of elastic instabilities in lid-driven cavity flow." Journal of Non-Newtonian Fluid Mechanics 94, no. 1 (November 2000): 15–35. http://dx.doi.org/10.1016/s0377-0257(00)00123-3.

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20

Peng, Yih-Ferng, Yuo-Hsien Shiau, and Robert R. Hwang. "Transition in a 2-D lid-driven cavity flow." Computers & Fluids 32, no. 3 (March 2003): 337–52. http://dx.doi.org/10.1016/s0045-7930(01)00053-6.

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21

Botella, O., and R. Peyret. "Benchmark spectral results on the lid-driven cavity flow." Computers & Fluids 27, no. 4 (May 1998): 421–33. http://dx.doi.org/10.1016/s0045-7930(98)00002-4.

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22

Kuhlmann, H. C., M. Wanschura, and H. J. Rath. "Elliptic instability in two-sided lid-driven cavity flow." European Journal of Mechanics - B/Fluids 17, no. 4 (July 1998): 561–69. http://dx.doi.org/10.1016/s0997-7546(98)80011-3.

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23

Albensoeder, S., and H. C. Kuhlmann. "Stability balloon for the double-lid-driven cavity flow." Physics of Fluids 15, no. 8 (August 2003): 2453–56. http://dx.doi.org/10.1063/1.1586270.

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24

Cortes, A. B., and J. D. Miller. "Numerical experiments with the lid driven cavity flow problem." Computers & Fluids 23, no. 8 (November 1994): 1005–27. http://dx.doi.org/10.1016/0045-7930(94)90002-7.

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25

Albensoeder, Stefan, and Hendrik C. Kuhlmann. "Accurate three-dimensional simulation of lid-driven cavity flow." PAMM 3, no. 1 (December 2003): 366–67. http://dx.doi.org/10.1002/pamm.200310455.

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26

Wang, C. Y. "Lid-driven Stokes slip flow in a rectangular cavity." European Journal of Mechanics - B/Fluids 89 (September 2021): 93–99. http://dx.doi.org/10.1016/j.euromechflu.2021.05.004.

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27

Huang, Tingting, and Hee-Chang Lim. "Simulation of Lid-Driven Cavity Flow with Internal Circular Obstacles." Applied Sciences 10, no. 13 (July 1, 2020): 4583. http://dx.doi.org/10.3390/app10134583.

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The Lattice Boltzmann method (LBM) has been applied for the simulation of lid-driven flows inside cavities with internal two-dimensional circular obstacles of various diameters under Reynolds numbers ranging from 100 to 5000. With the LBM, a simplified square cross-sectional cavity was used and a single relaxation time model was employed to simulate complex fluid flow around the obstacles inside the cavity. In order to made better convergence, well-posed boundary conditions should be defined in the domain, such as no-slip conditions on the side and bottom solid-wall surfaces as well as the surface of obstacles and uniform horizontal velocity at the top of the cavity. This study focused on the flow inside a square cavity with internal obstacles with the objective of observing the effect of the Reynolds number and size of the internal obstacles on the flow characteristics and primary/secondary vortex formation. The current LBM has been successfully used to precisely simulate and visualize the primary and secondary vortices inside the cavity. In order to validate the results of this study, the results were compared with existing data. In the case of a cavity without any obstacles, as the Reynolds number increases, the primary vortices move toward the center of the cavity, and the secondary vortices at the bottom corners increase in size. In the case of the cavity with internal obstacles, as the Reynolds number increases, the secondary vortices close to the internal obstacle become smaller owing to the strong primary vortices. In contrast, depending on the sizes of the obstacles ( R / L = 1/16, 1/6, 1/4, and 2/5), secondary vortices are induced at each corner of the cavity and remain stationary, but the secondary vortices close to the top of the obstacle become larger as the size of the obstacle increases.

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28

Chiang, T. P., Robert R. Hwang, and W. H. Sheu. "On End-Wall Corner Vortices in a Lid-Driven Cavity." Journal of Fluids Engineering 119, no. 1 (March 1, 1997): 201–4. http://dx.doi.org/10.1115/1.2819111.

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We conducted a flow simulation to study the laminar flow in a three-dimensional rectangular cavity. The ratio of cavity depth to width is 1:1, and the span to width aspect ratio (SAR) is 3:1. The governing equations defined on staggered grids were solved in a transient context by using a finite volume method, in conjunction with a segregated solution algorithm. Of the most apparent manifestation of three-dimensional characteristics, we addressed in this study the formation of corner vortices and its role in aiding the transport of fluid flows in the primary eddy and the secondary eddies.

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29

Wang, Chao, Jinju Sun, and Yan Ba. "A semi-Lagrangian Vortex-In-Cell method and its application to high-Re lid-driven cavity flow." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 6 (June 5, 2017): 1186–214. http://dx.doi.org/10.1108/hff-08-2015-0320.

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Purpose The purpose of this paper is to develop a Vortex-In-Cell (VIC) method with the semi-Lagrangian scheme and apply it to the high-Re lid-driven cavity flow. Design/methodology/approach The VIC method is developed for simulating high Reynolds number incompressible flow. A semi-Lagrangian scheme is incorporated in the convection term to produce unconditional stability, which gets rid of the constraint of the convection Courant-Friedrichs-Lewy (CFL) condition; the adaptive time step is used to maintain the numerical stability of the diffusion term; and the velocity boundary condition is readily converted to the vorticity formulation to suit discontinuous boundary treatment. The VIC simulation results are compared with those produced by other gird methods reported in open literature studies. Findings The lid-driven cavity flow is simulated from Re = 100 to 100,000. Similar vortex birth mechanisms are exhibited though, but distinct flow characteristics are revealed. At Re = 100 to 7,500, the cavity flow is confirmed steady. At Re = 10,000, 15,000 and 20,000, the cavity flow is periodical with a primary vortex held spatially at the center. In particular, at Re = 100,000 highly turbulent characteristics is first revealed and an analogous primary vortex is formed but in motion rather than stationary, which is caused by the considerable flow separation at all the boundaries. Originality/value In the lid-driven cavity, the flow becomes extremely complex and highly turbulent at Re = 100,000, and the analogous primary vortex structure is observed. Boundary layer separation is observed at all walls, producing small vortices and causing the displacement of the analogous primary vortex. Such a finding original and has not yet been reported by other investigators. It may provide a basis for conducting in-depth studies of the lid-driven cavity flow.

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30

Chen, Kuen Tsann, Chih Ching Tsai, and Win Jet Luo. "Multiplicity Flow Solutions in a Four-Sided Lid-Driven Cavity." Applied Mechanics and Materials 368-370 (August 2013): 838–43. http://dx.doi.org/10.4028/www.scientific.net/amm.368-370.838.

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In this study, the continuation method was adopted to explore the flow field states and flow bifurcation of incompressible flow in a four-sided lid-driven square cavity. The four plates moved at the same velocity and the opposite plates moved in opposite directions to drive the fluid in the cavity to flow. The flow bifurcation of the cavity flow when changing the driving velocity of the four plates simultaneously was discussed. The Reynolds number ranges of stable and unstable multiple solutions were determined from linear stability analysis of the obtained state solution. When the aspect ratio was 1 and the four plates were driven under the same velocity simultaneously, there were two pitchfork bifurcation points and two turning points in the flow bifurcation. Between the bifurcation points and turning points, there were two stable asymmetric solutions and one unstable symmetric solution existing. The flow bifurcation of the four-sided lid-driven cavity flow was analyzed by changing the driving velocity of two side plates when the top and bottom plates moved at the same velocity in opposite directions. According to the numerical results, when the Reynolds number of the top and bottom plates was fixed at 250 and the driving velocity of two side plates was changed, there were two non-crossing solution branches in the flow bifurcation, and one solution branch had strongly asymmetric stable solution. The other solution branch existed in the whole range of Reynolds number, and had one asymmetric stable solution. According to the bifurcation diagram, there were two asymmetric stable solutions and one symmetric unstable solution in the region of Reynolds number greater than 144, and there was only one asymmetric stable solution in the region of Reynolds number less than or equal to 144.

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31

Che Sidik, Nor Azwadi, and Siti Aisyah Razali. "Two-Sided Lid-Driven Cavity Flow at Different Speed Ratio by Lattice Boltzmann Method." Applied Mechanics and Materials 554 (June 2014): 675–79. http://dx.doi.org/10.4028/www.scientific.net/amm.554.675.

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In this study, the Lattice Boltzmann method has been used to investigate flow configuration of the two-sided lid driven cavity. The top and bottom lid were moved at the same direction but with different speed ratio which varies from 0 to 1. The range of Reynolds number is 100,400 and 1000. The results show that the increase in both speed ratio and Reynolds number give an effect on flow configuration of the cavity.

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32

SHAMEKHI, ABAZAR, and KAYVAN SADEGHY. "LID-DRIVEN CAVITY SIMULATION BY MESH-FREE METHOD." International Journal of Computational Methods 04, no. 03 (September 2007): 397–415. http://dx.doi.org/10.1142/s0219876207001230.

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In this work mesh-free method is used for solving two dimensional lid-driven cavity flow in a wide range of Reynolds numbers. The algorithm of mesh-free characteristic based split has been employed for this purpose. The results obtained from mesh-free characteristic based split algorithm have been compared to those of the finite element. The effect of using different shape functions on accuracy and stability of solution has been discussed. The sensitivity of stability of solution to nodes irregularity has been investigated. The effects of number of Gaussian integration points on the accuracy have been discussed.

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33

Srinivas, Garepally, A. V. Ramana Kumari, and Narayana Vekamulla. "Isotherms and Streamlines for 2D Lid Driven Square Cavity." International Journal of Innovative Technology and Exploring Engineering 10, no. 11 (September 30, 2021): 97–99. http://dx.doi.org/10.35940/ijitee.k9502.09101121.

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Analysis of lid driven square cavity flow of air with three different ranges of Ri and Re are analyzed using numerically. Adiabatic temperature is maintained at horizontal walls and isothermal temperature is established at the vertical walls in which the top wall is assumed to slide with a uniform speed. Finite volume method techniques have used to solve non dimensional governing equations. To visualize the flow and thermal characteristics, the control parameters, the Richardson number (Ri) and Reynolds number (Re) and in the range of 0.001 ≤ Ri ≤ 10 and 100 ≤ Re ≤ 400 are used for streamlines and isotherms.

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34

Bastl, Bohumír, Marek Brandner, Jiří Egermaier, Hana Horníková, Kristýna Michálková, and Eva Turnerová. "NUMERICAL SIMULATION OF LID-DRIVEN CAVITY FLOW BY ISOGEOMETRIC ANALYSIS." Acta Polytechnica 61, SI (February 10, 2021): 33–48. http://dx.doi.org/10.14311/ap.2021.61.0033.

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In this paper, we present numerical results obtained by an in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the standard benchmark problem for incompressible fluid flow simulation – lid-driven cavity flow. The steady Navier-Stokes equations are solved in their velocity-pressure formulation and we consider only inf-sup stable pairs of B-spline discretization spaces. The main aim of the paper is to compare the results from our IgA-based flow solver with the results obtained by a standard package based on finite element method with respect to degrees of freedom and stability of the solution. Further, the effectiveness of the recently introduced rIgA method for the steady Navier-Stokes equations is studied.The authors dedicate the paper to Professor K. Kozel on the occasion of his 80th birthday.

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35

Wu, Ke, Bruno D. Welfert, and Juan M. Lopez. "Complex dynamics in a stratified lid-driven square cavity flow." Journal of Fluid Mechanics 855 (September 20, 2018): 43–66. http://dx.doi.org/10.1017/jfm.2018.656.

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The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier–Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.

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36

Narayana, Vekamulla. "Visualization Techniques of Differentially Heated Lid-Driven Square Cavity." International Journal of Mathematics and Mathematical Sciences 2020 (March 9, 2020): 1–7. http://dx.doi.org/10.1155/2020/5756764.

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In the present study, an attempt is made to explore the flow field inside the differentially heated lid-driven square cavity. The governing equations along with boundary conditions are solved numerically. The simulated results (100 ≤ Re ≤ 1000 and 0.001 ≤ Ri ≤ 10) are validated with previous results in the literature. The convection differencing schemes, namely, UPWIND, QUICK, SUPERBEE, and SFCD, are discussed and are used to simulate the flow using the MPI code. It is observed that the computational cost for all the differencing schemes get reduced tremendously when the MPI code is implemented. Plots demonstrate the influences of Re and Ri in terms of the contours of the fluid streamlines, isotherms, energy streamlines, and field synergy principle.

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37

Mitsoulis, E., and Th Zisis. "Flow of Bingham plastics in a lid-driven square cavity." Journal of Non-Newtonian Fluid Mechanics 101, no. 1-3 (November 2001): 173–80. http://dx.doi.org/10.1016/s0377-0257(01)00147-1.

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38

Biswas, Nirmalendu, and Nirmal K. Manna. "Magneto-hydrodynamic Marangoni flow in bottom-heated lid-driven cavity." Journal of Molecular Liquids 251 (February 2018): 249–66. http://dx.doi.org/10.1016/j.molliq.2017.12.053.

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39

Garcia, Salvador. "Hopf Bifurcations, Drops in the Lid-Driven Square Cavity Flow." Advances in Applied Mathematics and Mechanics 1, no. 4 (June 2009): 546–72. http://dx.doi.org/10.4208/aamm.09-m0924.

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40

Sheu, T. W. H., and S. F. Tsai. "Flow topology in a steady three-dimensional lid-driven cavity." Computers & Fluids 31, no. 8 (November 2002): 911–34. http://dx.doi.org/10.1016/s0045-7930(01)00083-4.

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41

Zhuo, Congshan, Chengwen Zhong, Xixiong Guo, and Jun Cao. "MRT-LBM Simulation of Four-lid-driven Cavity Flow Bifurcation." Procedia Engineering 61 (2013): 100–107. http://dx.doi.org/10.1016/j.proeng.2013.07.100.

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42

Romanò, Francesco, Tuǧçe Türkbay, and Hendrik C. Kuhlmann. "Lagrangian chaos in steady three-dimensional lid-driven cavity flow." Chaos: An Interdisciplinary Journal of Nonlinear Science 30, no. 7 (July 2020): 073121. http://dx.doi.org/10.1063/5.0005792.

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43

ALBENSOEDER, S., and H. C. KUHLMANN. "Nonlinear three-dimensional flow in the lid-driven square cavity." Journal of Fluid Mechanics 569 (November 15, 2006): 465. http://dx.doi.org/10.1017/s0022112006002758.

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44

Albensoeder, S., H. C. Kuhlmann, and H. J. Rath. "The lid-driven cavity revisited: Stability of two-dimensional flow." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 81, S3 (2001): 779–80. http://dx.doi.org/10.1002/zamm.200108115162.

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45

Venkatadri, K., S. Maheswari, C. Venkata Lakshmi, and V. Ramachandra Prasad. "Numerical simulation of lid-driven cavity flow of micropolar fluid." IOP Conference Series: Materials Science and Engineering 402 (September 20, 2018): 012168. http://dx.doi.org/10.1088/1757-899x/402/1/012168.

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46

Tsorng, S. J., H. Capart, D. C. Lo, J. S. Lai, and D. L. Young. "Behaviour of macroscopic rigid spheres in lid-driven cavity flow." International Journal of Multiphase Flow 34, no. 1 (January 2008): 76–101. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2007.06.007.

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47

Kim, You-Gon. "Digital vector image processing of lid-driven rotating cavity flow." KSME Journal 9, no. 2 (June 1995): 187–96. http://dx.doi.org/10.1007/bf02953620.

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48

Azzouz, El Amin, and Samir Houat. "Asymmetrical Flow Driving in Two-Sided Lid-Driven Square Cavity with Antiparallel Wall Motion." MATEC Web of Conferences 330 (2020): 01009. http://dx.doi.org/10.1051/matecconf/202033001009.

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Abstract:

The two-dimensional flow in a two-sided lid-driven cavity is often handled numerically for the same imposed wall velocities (symmetrical driving) either for parallel or antiparallel wall motion. However, in this study, we present a finite volume method (FVM) based on the second scheme of accuracy to numerically explore the steady two-dimensional flow in a two-sided lid-driven square cavity for antiparallel wall motion with different imposed wall velocities (asymmetrical driving). The top and the bottom walls of the cavity slide in opposite directions simultaneously at different velocities related to various imposed velocity ratios, λ = -2, -6, and -10, while the two remaining vertical walls are stationary. The results show that varying the velocity ratio and consequently the Reynolds ratios have a significant effect on the flow structures and fluid properties inside the cavity.

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Chourushi, T., S. Singh, and R. S. Myong. "COMPUTATIONAL STUDY OF RAREFIED FLOW INSIDE A LID DRIVEN CAVITY USING A MIXED MODAL DISCONTINUOUS GALERKIN METHOD." Journal of Computational Fluids Engineering 23, no. 3 (September 30, 2018): 62–71. http://dx.doi.org/10.6112/kscfe.2018.23.3.062.

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50

GONZÁLEZ, L. M., M. AHMED, J. KÜHNEN, H. C. KUHLMANN, and V. THEOFILIS. "Three-dimensional flow instability in a lid-driven isosceles triangular cavity." Journal of Fluid Mechanics 675 (March 22, 2011): 369–96. http://dx.doi.org/10.1017/s002211201100022x.

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Abstract:

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

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