• Transactions of the Korean Society of Mechanical Engineers B
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• v.39 no.5
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• pp.415-423
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• 2015

In this study, we present a grid refinement model in the lattice Boltzmann method (LBM) for two-dimensional incompressible fluid flow. That is, the model combines the desirable features of the lattice Boltzmann method and stream function-vorticity formulations. In order to obtain an accurate result, very fine grid (or lattice) is required near the solid boundary. Therefore, the grid refinement model is used in the lattice Boltzmann method for stream function-vorticity formulation. This approach is more efficient in that it can obtain the same accurate solution as that in single-block approach even if few lattices are used for computation. In order to validate the grid refinement approach for the stream function-vorticity formulation, the numerical simulations of lid-driven cavity flows were performed and good results were obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.111-133
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• 2000

A Legendre spectral tau approximation scheme for solving the two-dimensional stationary incompressible Stokes equations is considered. Based on the vorticity-stream function formulation and variational forms, boundary value and normal derivative of vorticity are computed. A factorization technique for matrix stems based on the Schur decomposition is derived. Several numerical experiments are performed.

• Journal of Ocean Engineering and Technology
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• v.34 no.2
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• pp.89-96
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• 2020

In this study, the Norbury-Fraenkel family of vortex rings is analyzed using a contour dynamics method for the stream function, which significantly reduces the numerical burden in the calculation. The stream function is formulated as the integral along the contour of the vorticity core. The integration over the logarithmic-singular segment is evaluated analytically, and the positions of the nodal points of the contour are calculated directly. The shapes of the cores and the dividing stream surfaces are found based on the mean core radius. Compared with other studies, the proposed method is verified and found to be more efficient.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.3
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• pp.575-581
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• 1988

To integrate the two-dimensional Navier-Stokes equations numerically in multiply-connected flow regions, the vorticity-stream function formulation is used. The steady stream function value at the surface of the multibody, initially unknown, has been determined interactively by introducing a line integral which requires the single-valuedness of pressure at each interaction step. This procedure is relatively simpler and more efficient than the primitive variable formulation which requires much more computing time and shows poor convergence. Three doubly-connected flow problems are defined and numerically analyzed by the present method. The results have been compared either with earlier existing ones or with the experimental interferograms to demon-strate the validity of the presented method.

• Water for future
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• v.21 no.3
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• pp.291-291
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• 1988

The two dimensional time dependent flow past a circular cylinder is analyzed numerically. In the analysis, equations of conservation of mass and momentum are transformed to equations of stream function-vorticity and vorticity transport, and nondimensionalized by nondimensional parameters representing flow characteristics, The resulting stream function-vorticity equstion and vorticity transport equation are solved by successive over relaxation scheme and alternating direct implicit scheme. Numerical experments are performed for the flow in the range of Reynolds number 125 to 275. The time dependent streamlines, vorticities, pressure on cylinder surface, separation angle, and drag and lift coefficients are calculated, and the method for estimation of pressure on cylinder surface and the outer boundary limit are developed.

• Water for future
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• v.31 no.4
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• pp.291-297
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• 1998

The two dimensional time dependent flow past a circular cylinder is analyzed numerically. In the analysis, equations of conservation of mass and momentum are transformed to equations of stream function-vorticity and vorticity transport, and nondimensionalized by nondimensional parameters representing flow characteristics, The resulting stream function-vorticity equation and vorticity transport equation are solved by successive over relaxation scheme and alternating direct implicit scheme. Numerical experiments are performed for the flow in the range of Reynolds number 125 to 275. The time dependent streamlines, vorticities, pressure on cylinder surface, separation angle, and drag and lift coefficients are calculated, and the method for estimation of pressure on cylinder surface and the outer boundary limit are developed.

• Journal of Electrical Engineering and Technology
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• v.4 no.2
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• pp.249-254
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• 2009

This article deals with the analysis of a coupling between stationary Maxwell's equations, the transient state Navier-Stokes and thermal equations. The resolution of these equations is obtained by introducing the magnetic vector potential A, the vorticity ${\xi}$, the stream function ${\psi}$ and the temperature T. The flux density, the electromagnetic thrust, the electric power density, the velocity, the pressure and the temperature are graphically visualized. Also, the influence of the frequency is presented.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.516-523
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• 2009

The artificial compressibility (AC) method for the incompressible Navier-Stokes equations in the generalized curvilinear coordinates using the primitive form is implemented. The main advantage of the AC approach is that the resulting system of equations resembles the system of compressible N-S equations and can thus be integrated in time using standard, well-established time-marching methods. The errors, which are the odd-even oscillation, for pressure field in using the artificial compressibility can be eliminated by using the $4^{th}$ order artificial dissipation term which is explicitly included. Even though this paper focuses exclusively on 2D laminar flows to validate and assess the performance of this solver, this numerical method is general enough so that it can be readily extended to carry out 3D URANS simulation of engineering flows. This algorithm yields practically identical velocity profiles and primary vortex and secondary vortices that are in excellent overall agreement with the results of the vorticity-stream function formulation (Ghia et al., 1982). However, the grid resolution have to be required to be large enough to express the various vortices.

• Journal of computational fluids engineering
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• v.7 no.3
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• pp.53-59
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• 2002

A two-dimensional laminar flow through a channel with a pair of symmetric vertical fins is investigated. At far up- and down-stream from the fins, the plane Poiseuille flow exists in the channel. The Stokes flow for this channel is first investigated analytically and then the other laminar flows by numerical method. For analytic method, the method of eigen function expansion and collocation method are employed. In numerical solution for laminar flows, finite difference method(FDM) is used to obtain vorticity and stream function. From the results, the streamline patterns are shown and the additional pressure drop due to the attached fins and the force exerted on the fin are calculated. It is clear that the force depends on the length of fins and Reynolds number. When the Reynolds number exceeds a critical value, the flow becomes asymmetric. This critical Reynolds number Re/sub c/ depends on the length of the fins.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.9
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• pp.2329-2338
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• 1993

An accurate analysis procedure to solve the flow about a flat plate at various incidences has been developed. The Navier-Stokes equations of stream function and vorticity form are solved in a sufficiently large computational domain, in which the grid lines are mutually orthogonal. The details of the flow near the singularity at the tip of the plate is well captured by the analytic solution which is asymptotically matched to the numerically generated outer solution. The solution for each region is obtained iteratively : the solution of one (inner or outer) region uses that of the other as the boundary condition after each cycle. The resulting procedure is accurate everywhere and also computationally efficient as the singularity has been removed. It is applied to the flat plate for a wide range of Re : the results agree very well with the existing computation and experiment.