• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.6
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• pp.1640-1647
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• 1993

The numerical diffusion arising from streamline-to-grid skewness produces a deteriorating effect on the numerical accuracy. The QUICKER scheme to reduce the numerical diffusion requires more computational effort than the HYBRID scheme. This paper deals with the relative computational efficiencies of adopting QUICKER scheme with a coarser grid system and of adopting HYBRID scheme with a denser grid system. Laminar driven cavity flow with Re=400, 1000 is used as a test problem. It is found that QUICKER scheme with a coarser grid system is more efficient than the HYBRID scheme with a denser grid system.

• Journal of Advanced Marine Engineering and Technology
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• v.23 no.2
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• pp.176-183
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• 1999

This paper is aimed to investigate behaviour of vortex in 2-D step cavity with high Reynolds numbers$(3.2{\times}10^{3},\;10^{4},\;3{\times}10^{4},\;5{\times}10^{4}\;and\;7{\times}10^{4})$. The SOLA algorithm which is MAC type was adopted to solution method computing the flow field on irregular grid. In case of $Re=7{\times}10^{4}$ flow behavior is steady bu periodic unsteady sinusoidal fluctuation of local velocity and kinetic energy is found for $Re=10^{4}$ Continuous movements of small eddies in the secondary flow regions are discov-ered for $3{\times}10^{4}$ Generation of eddies and their active migrating behavior are detected over $Re=5{\times}10^{4}$ resulting in complete unsteady and non-linear flow characteristics Furthermore a typhoon-like vortex(TLV) appears intermittently and rotates along the separation regions and boundary layers.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2077-2081
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• 2005

A symmetry breaking nonlinear fluid flow in a two-dimensional wall-driven square cavity taking symmetric boundary condition after some transients has been investigated numerically. It has been shown that the symmetry breaking critical Reynolds number is dependent on the time history of the boundary condition. The cavity has at least three stable steady state solutions for Re=300-375, and two stable solutions if Re>400. Also, it has also been showed that a particular solution among several possible solutions can be obtained by a controlled boundary condition.

• Journal of Advanced Marine Engineering and Technology
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• v.21 no.4
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• pp.430-436
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• 1997

Time-dependent Flow characteristics of a two-dimensional lid-driven square cavity flow of six high Reynolds numbers, $10^4 2{\times}lO^4., 3{\times}l0^4, 5{\times}lO^4, 7.5{\times}lO^4$ and $10^5$ were investigated. A convection conservative difference scheme based upon SOLA to maintain the nearly 2nd-order spatial accuracy was adopted on irregular grid formation. Irregular grid number is $80{\times}80$ and its minimum size is about 1/400 of the cavity height(H) and its maximum is about 1/53 H. The result shows that at Re= $10^4$, periodic migration of small eddies appearing in corner separation region and its temporal sinusoidal fluctuation are represented. And another critical Reynolds number which shows the commencement of flow randomness emerging from the periodic fluctuation is assumed to be around Re= $1.5{\times}10$. At five higher Reynolds numbers ($2{\times}lO^4., 3{\times}l0^4, 5{\times}lO^4, 7.5{\times}lO^4$ and $10^5$), an organizing structure of four consecutive vortices similar to a Moffat vortex at two lower corners is revealed from time-mean flow patterns.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.65.1-65.1
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• 2005

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.131-133
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• 2003

The streamfunction-vorticity equations for two-dimentional cavity flow are solved by a new finite element method which uses finite spectral basis functions as interpolation functions for rectangular elements. Results for several cases with different Renold's number are compared with benchmark solutions and found to be in well agreement.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.6
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• pp.1179-1194
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• 1992

QUICKER scheme has several attractive properties. However, under highly convective conditions, it produces overshoots and possibly some oscillations on each side of steps in the dependent variable when the flow is convected at an angle oblique to the grid line. Fortunately, it is possible to modify the QUICKER scheme using non-linear and linear functional relationship. Details of the development of polynomial upwinding scheme are given in this paper, where it is seen that this non-linear scheme has also third order accuracy. This polynomial upwinding scheme is used as the basis for the SHARPER and SMARTER schemes. Another revised scheme was developed by partial modification of QUICKER scheme using CDS and UPWIND schemes(QUICKUP). These revised schemes are tested at the well known bench mark flows, Two-Dimensional Pure Convection Flows in Oblique-Step, Lid Driven Cavity Flows and Buoyancy Driven Cavity Flows. For pure convection oblique step flow test problem, QUICKUP, SMARTER and SHARPER schemes remain absolutely monotonic without overshoot and oscillation. QUICKUP scheme is more accurate than any other scheme in their relative accuracy. In high Reynolds number Lid Driven Cavity Flow, SMARTER and SHARPER schemes retain lower computational cost than QUICKER and QUICKUP schemes, but computed velocity values in the revised schemes produced less predicted values than QUICKER scheme which is strongly effected by overshoot and undershoot values. Also, in Buoyancy Driven Cavity Flow, SMARTER, SHARPER and QUICKUP schemes give acceptable results.

• Journal of computational fluids engineering
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• v.3 no.1
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• pp.11-21
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• 1998

A vorticity-based method for the numerical solution of the two-dimensional incompressible Navier-Stokes equations is presented. The governing equations for vorticity, velocity and pressure variables are expressed in an integro-differential form. The global coupling between the vorticity and the pressure boundary conditions is fully considered in an iterative procedure when numerical schemes are employed. The finite volume method of the second order TVD scheme is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition. The velocity field is obtained by using the Biot-Savart integral. The Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well established for potential flow analysis. The present formulation is validated by comparison with data from the literature for the two-dimensional cavity flow driven by shear in a square cavity. We take two types of the cavity now: (ⅰ) driven by non-uniform shear on top lid and body forces for which the exact solution exists, and (ⅱ) driven only by uniform shear (of the classical type).

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.3
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• pp.624-634
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• 1994

A numerical method which combines equal-order velocity-pressure formulation originated from SIMPLE algorithm and streamline upwinding method has been developed. To verify the proposed numerical method, we considered the lid-driven cavity flow and backward facing step flow. The trend of convergence history is stable up to the error criterion beyond which the maximum value of error is oscillatory due4 to the round-off error. In the present study, all results were obtained with the single precision calculation up to the given error criterion and it was found to be sufficient for our purpose. The present results were then compared with existing experimental results using laser doppler velocimetry and numerical results using finite difference method and mixed interpolation finite element method. It has been shown that the present method gives accurate results with less memories and execution time than the coventional finite element method.

• Journal of the Korean Society of Visualization
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• v.9 no.3
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• pp.44-50
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• 2011

In this study, we propose a method for characterizing fluid-mechanical properties of a fluid surface, such as surface dilatational and shear viscosity, by matching the flow visualization and the numerical simulation for a Stokes flow in a three-dimensional cavity. The surface flow is driven by shear stress exerted on the free surface by an external gas flow. The external gas flow is simulated by using a commercial code, while the Stokes flow is calculated by an in-house code. We have found that the surface flow is very sensitive to the surface tension and other properties. The qualitative feature of the surface flow can be reproduced by the parameter tuning.