• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.153-158
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• 2005

Numerical simulations of two-dimensional steady incompressible lid-driven flow in a square cavity are presented to verify the validity of a new solution code(PowerCFD) with unstructured grids. The code uses the non-staggered(collocated) grid approach which is very popular for incompressible flow analysis because of its numerical efficiency on the curvilinear or unstructured grids. Solutions are obtained for configurations with a Reynolds number as high as 10,000 with both rectangular and hybrid types of unstructured grid mesh. Interesting features of the flow are presented in detail and comparisons are made with benchmark solutions found in the literature. It is found that the code is capable of producing accurately the nature of the lid-driven cavity flow at high Reynolds numbers.

• Journal of computational fluids engineering
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• v.10 no.4 s.31
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• pp.18-23
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• 2005

Numerical simulations of two-dimensional steady incompressible lid-driven flow in a square cavity are presented by a new solution code(PowerCFD) which adopts an unstructured cell-centered method. Solutions are obtained for configurations with a Reynolds number as high as 10,000 with both rectangular and hybrid types of unstructured grid mesh in order to validate the code's independency of grid type. Interesting features of the flow are presented in detail and comparisons are made with benchmark solutions found in the literature. It is found that the code is capable of producing accurately the nature of the lid-driven cavity flow at high Reynolds numbers with no grid type dependency.

• Journal of the Korean Society of Visualization
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• v.18 no.3
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• pp.42-51
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• 2020

This study performs a numerical simulation of lid driven rectangular cavity flow with different aspect ratios of k = 0.5 to 4 under Reynolds 100, 1,000, 10,000 by using multi-relaxation time (MRT) Lattice Boltzmann Method (LBM). In order to achieve better convergence, well-posed boundary conditions in the domain should be defined such as no-slip condition on side and bottom solid wall surfaces and uniform horizontal velocity on the top of the cavity. This study focuses on the flow inside different shape of rectangular cavity with the aim to observe the effect of the Reynolds number and aspect ratio on the flow characteristics and primary/secondary vortex formation. In order to validate the study, the results have been compared with existing works. The result shows that the Reynolds number and the aspect ratio both has substantial effects on the flow inside the lid-driven rectangular cavity.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.11
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• pp.2971-2980
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• 1995

A numerical study of fluid flow in driven cavity was carried out using singular finite element method. The driven cavity problem is known to have infinite velocity gradients as well as dual velocity conditions at the singular points. To overcome such difficulties, a finite element method with singular shape functions was used and a special technique was employed to allow multiple values of velocities at the singular points. Application of singular elements in the driven cavity problem has a significant influence on the stability of solution. It was found the singular elements gave a stable solution, especially, for the pressure distribution of the entire flow field by keeping up a large pressure at the singular points. In the existing solutions of driven cavity problem, most efforts were focused on the study of streamlines and vorticities, and pressure were seldom mentioned. In this study, however, more attention was given to the pressure distribution. Computations showed that pressure decreased very rapidly as the distance from the singular point increased. Also, the pressure distribution along the vertical walls showed a smoother transition with singular elements compared to those of conventional method. At the singular point toward the flow direction showed more pressure increase compared with the other side as Reynolds number increased.

• Journal of computational fluids engineering
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• v.11 no.3 s.34
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• pp.37-45
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• 2006

In this study we present the numerical methods that can be used in visualization of the flow and mixing patterns in a cavity driven by a top lid. The basic flow field within the cavity has been obtained by using a simple numerical scheme. The invariant manifold also called unstable manifold was then attained to represent the mixing pattern within the cavity. It was shown that care must be taken in calculating the trajectories of the fluid particles especially near corners of the cavity. The numerical results show excellent agreement with those obtained experimentally by other research group.

• Journal of Ocean Engineering and Technology
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• v.12 no.1
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• pp.113-119
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• 1998

An experimental study was carried out in a three-dimensional cubic cavity driven by 2-dimensional plane Poiseuille flow for three kinds of Reynolds number, $10^4$, 3 $\times$ $10^4$ and 5 $\times$ $10^4$ based on the cavity width and cavity inlet mean flow velcoity. Instant simultaneous velocity vectors at whole field were measured by 2-D PIV system. Laser based illumination and two-frame grey-level cross correlation algorithm are adopted. Severe unsteady flow fluctuation within the cavity are remarkable at above Re = 3 $\times$ $10^4$ Reynolds numbers and sheared mixing layer phenomena are also found at the region where inlet driving Poiseuille flow is collided with the clock-wise rotating main primary vortex at upper center area. Instant velocity profiles reveal that deformed forced vortex formation is observed throughout the separate two areas.

• Journal of Advanced Marine Engineering and Technology
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• v.22 no.6
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• pp.935-941
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• 1998

Experiments were carried out for a cubic cavity flow. Contrinuous shear stress is supplied by driven flow for high Reynolds number and three kinds of aspect ratios. Velocity vectors are obtained by PIV and they are used as velocity components for Poisson equation for pressure, Related boundary conditions and no-slip condition at solid wall and the linear velocity extrapolation on the upper side of cavity are well examined for the present study. For calculation of pressure resolution of grid is basically $40{\times}40$ and 2-dimensional uniform mesh using MSC staggered grid is adopted. The flow field within the cavity maintains a forced-vortex formation and almost of the shear stress from the driving inflow is transformed into rotating flow energy and the size of the distorted forced-vortex increases with increment of Reynolds number

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.537-547
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• 1995

Numerical study on the chaotic stirring of viscous flow in an alternately driven cavity has been performed. Even under the Stokes-flow assumption, the inherent singularity at the corners made the problem not so easily accessible. With some special treatments to the region near the corners, the biharmonic equation was solved numerically by using the fully implicit method. The velocity field was then used in obtaining the trajectories of passive particles for studying the stirring effect. The three tools developed in the field of the nonlinear dynamics and chaos, that are the Poincare sections, the unstable manifolds, and the Lyapunov exponents, were used in analysing the stirring effect. It was shown that the unstable manifolds obtained in this study well fit the experimental results given by the previous investigators. It is predicted that the best stirring can be obtained when the aspect ratio a is near 0.8 and the dimensionless period T is in the range 4.3 - 4.7.

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.83-84
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• 2006

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.291-301
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• 1999

We study an optimal control problem of the fluid flow governed by the navier-Stokes equations. The control problem is formulated with the flow in the driven cavity. Existence of an optimal solution and first-order optimality condition of the optimal control are derived. We report the numerical results for the finite eleme수 approximations of the optimal solutions.