• Journal of Advanced Marine Engineering and Technology
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• v.20 no.3
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• pp.101-109
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• 1996

Two-dimensional lid-driven closed flows within square cavity were studied numerically for four Reynolds numbers : $10^4$, 3$\times10^4$, 5$\times10^4$ and 7.5$\times10^4$. A convective difference scheme to maintain the same spatial accurary by irregular grid correction is adopted by applying the interior division principle. Grid number is $80\times80$and its minimum size is about 1/400 of the cavity height. At Re=$10^4$, periodic migration of small eddies appearing in corner separation region and its temporal sinusoidal fluctuation are represented. At three higher Reynolds numbers(3$\times10^4$, 5$\times10^4$ and 7.5$\times10^4$), an organizing structure of four consecutive vorticles at two lower corners is revealed from time-mean flow patterns. But, instantaneous flow characteristics show very random unsteady fluctuation mainly due to the interaction between rotating shed vortices and stationary eddies within the corners.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1875-1879
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• 2004

This paper deals with the evaluation of several boundary conditions which are commonly used in the lattice Boltzmann equation method. 2-D channel flow(poiseui1le flow) and lid-driven cavity flow was selected as a test problem of this study, because there exist an analytic solution and previous study which could be used for a benchmarking test. It was found that lattice Boltzmann method still needs more considerations of stability and physical consistency, though it could predict the flow patterns both qualitatively and quantitatively.

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1730-1740
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• 2006

A nodeless variables finite element method for analysis of two-dimensional, steady-state viscous incompressible flow is presented. The finite element equations are derived from the governing Navier-Stokes differential equations and a corresponding computer program is developed. The proposed method is evaluated by solving the examples of the lubricant flow in journal bearing and the flow in the lid-driven cavity. An adaptive meshing technique is incorporated to improve the solution accuracy and, at the same time, to reduce the analysis computational time. The efficiency of the combined adaptive meshing technique and the nodeless variables finite element method is illustrated by using the example of the flow past two fences in a channel.

• Journal of computational fluids engineering
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• v.13 no.4
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• pp.13-23
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• 2008

This paper is an extension of previous study[1] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite (serendipity) cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires four degrees-of-freedom at each element corners. Those degrees-of-freedom are the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational basis functions from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[2].

• Wind and Structures
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• v.14 no.5
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• pp.465-480
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• 2011

In this paper, a stabilized large eddy simulation technique is developed to predict turbulent flow with high Reynolds number. Streamline Upwind Petrov-Galerkin (SUPG) stabilized method and three-step technique are both implemented for the finite element formulation of Smagorinsky sub-grid scale (SGS) model. Temporal discretization is performed using three-step technique with viscous term treated implicitly. And the pressure is computed from Poisson equation derived from the incompressible condition. Then two numerical examples of turbulent flow with high Reynolds number are discussed. One is lid driven flow at Re = $10^5$ in a triangular cavity, the other is turbulent flow past a square cylinder at Re = 22000. Results show that the present technique can effectively suppress the instabilities of turbulent flow caused by traditional FEM and well predict the unsteady flow even with coarse mesh.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.5
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• pp.675-684
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• 2002

Two-dimensional, angle-resolved LDV(Laser Doppler Velocimetry) measurements of the turbulent rotating flow field in a confined cylinder have been performed. The configurations of interest are flows between a rotating upper disk with a rod attached by a disk or impeller($\theta$ = 45$^{\circ}$, 90$^{\circ}$) and a stationary lower disk in a confined cylinder. The mean flow velocity as well as the turbulent intensity of the flow field have been measured. The results show that the flow is strongly dependent on the position of the impellers or the disk, negligibly affected by the Reynolds number in turbulent flow. It is observed that the mixing effect of the axial flow impeller($\theta$ = 45$^{\circ}$) is better than that of the radial flow impeller($\theta$ = 90$^{\circ}$) or a disk.

• Journal of Advanced Marine Engineering and Technology
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• v.23 no.6
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• pp.770-777
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• 1999

In this study a phase diagram has been used to investigate the unsteadiness of two-dimensional lid-driven closed flows within a square cavity for twelve Reynolds numbers; $7.5{\times}10^3,\; 8{\times}10^3,\; 8.5{\times}10^3,\; 9{\times}10^3,\; 9.5{\times}10^3,\; 10^4,\;1.5{\times}10^4,\;2{\times}10^4,\; 3{\times}10^4,\; 7.5{\times}10^4$ and $10^5$. The results indicate that the first critical Reynolds number at which the flow unsteadiness of sinusoidal fluctuation appears from the temporal variation of total kinetic energy curves is assumed of sinusoidal fluctuation appears form the temporal variation of total kinetic energy curves is assumed to be in the neigh-bourhood of $Re=8.5{\times}10^3$ The second critical Reynolds number where the periodic amplitude and frequency collapse to random disturbance being existed around $Re=1.5{\times}10^4$ The exponentially decreasing vortices formed at the lower two corners are found commonly at the time-mean flow pattern of $Re=3{\times}10^4$.