• Journal of the Korean Institute of Navigation
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• v.9 no.2
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• pp.43-63
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• 1985

As a circular cylinder has a comparatively simple shape and becomes a basic problem for flows around other various shapes of bodies, the problem of two-dimensional viscous flow around the circular cylinder has been investigated, both theoretically and experimentally. But not a few problems are left unsolved. It is well known that the calculations are successfully made with the approximations of Stokes or Oseen for very low Reynolds numbers, but as Reynolds number is increased, Oseen's approximations as well as Stokes's ones become more and more remote from the exact solution of the Navier-Stokes equations. Therefore, in this paper, the authors transform the Navier-Stokes equations into the finite difference equations in the steady two-dimensional viscous flow at Reynolds number up to 45, and then solve the solution of the Navier-Stokes equations numerically. Also, the authors examine the accuracy of the solution by means of flow visualization with aluminum powder. The main results are as follows; (1) The critical Reynolds number at which twin vortices begin to form in the rear of the circular cylinder is found to be 6 in the experiment and 4 in the numerical solution. (2) As Reynolds number is increased, it is proved that the ratio of the length of the twin vortices to the diameter is grown almost linearly, both experimentally and numerically. (3) Separation angle is also increased according to reynolds number. But it is found that it would converge into 101.3 degrees, both experimentally and numerically.

• Journal of the Korean Society of Hazard Mitigation
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• v.4 no.2 s.13
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• pp.71-76
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• 2004

To investigate the inundation of tsunamis in the vicinity of a circular island, a numerical model has been developed based on quadtree grids. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using a finite difference leap-frog scheme on adaptive hierarchical quadtree grids. The quadtree grids are generated around a circular island where refined with rectangular or circular domain. Obtained numerical results have been verified by comparing to available laboratory measurements of run-up heights. A good agreement has been achieved.

• STI Policy Review
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• v.6 no.1
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• pp.1-23
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• 2015

Based on the work of Anand et al. (2013) we measure inclusive income growth, which combines growth in gross domestic product (GDP) per capita and growth in the equity of the income distribution. Extending the work of Causa et al. (2014), we estimate a dynamic simultaneous structural equations model of GDP per capita and inclusive income on panel data for 63 countries over the 1990-2013 period. We estimate both equations in error correction form by difference GMM (generalized method of moments). Among the explanatory variables of the level and the distribution of GDP per capita we include R&D (research and development) expenditure per capita. In OECD countries we obtain a large positive effect of R&D on GDP. R&D is found to have a positive effect on the social mobility index but its impact on the income equity index at first decreases, then switches around to become slightly positive in the long run. In non- OECD countries, R&D is found to decrease inclusive income, mostly through a negative growth effect but also because of a slightly increasing income inequity effect.

• Convergence Security Journal
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• v.5 no.3
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• pp.93-97
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• 2005

MacCormack's method is an explicit, second order finite difference scheme that is widely used in the solution of hyperbolic partial differential equations. Apparently, however, it has shown entropy violations under small discontinuity. This non-physical shock grows fast and eventually all the meaningful information of the solution disappears. Some modifications of MacCormack's methods follow ideas of central schemes with an advantage of second order accuracy for space and conserve the high order accuracy for time step also. Numerical results are shown to perform well for the one-dimensional Burgers' equation and Euler equations gas dynamic.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.5
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• pp.755-761
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• 1987

Two-Dimensional incompressible laminar boundary layer with the reversed flow region is computed using the parially parabolized Navier-Stokes equations in primitive variables. The velocities and the pressure are explicity coupled in the difference equation and the resulting penta-diagonal matrix equations are solved by a streamwise marching technique. The test calculations for the trailing edge region of a finite flat plate and Howarth's linearly retarding flows demonstrate that the method is accurate, efficient and capable of predicting the reversed flow region.

• Water for future
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• v.23 no.2
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• pp.251-263
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• 1990

For surcharge flow in a sewer, the slot technique simulates surcharge flow as open - channel flow using a hypothetical narrow open piezometric slot at the sewer crown. The flow in a sewer is described mathematically using the unsteady open - channel Saint-Venant equations. In this study, the computer simulation model(USS-slot) using slot techniques is develeped to simulate the inlet hydrographs to manholes and the flow under pressure as well as free - surface flow in tree - type sewer networks of circular conduits. The inlet hydrographs are simulated by using the rational method or the ILSD progrm. The Saint-Venant equations for unsteady open - channel flow in seweres are solved by using a four - point implicit difference scheme. The flow equations of the sewers and the junction flow equations are solved simulaneously using a sparse matrix solution technique.

• Transactions of the Society of Information Storage Systems
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• v.5 no.1
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• pp.19-35
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• 2009

The present work is an experimental and analytical study on a flexible disk rotating close to a rigid rotating disk in open air. In the analytical study, the air flow in the gap between the flexible disk and the rigid disk is modeled using Navier-Stokes and continuity equations while the flexible disk is modeled using the linear plate theory. The flow equations are discretized using the cell centered finite volume method (FVM) and solved numerically with semi-implicit pressure-linked equations (SIMPLE algorithm). The spatial terms in the disk equation are discretized using the finite difference method (FDM) and the time integration is performed using fourth-order Runge-Kutta method. An experimental test-rig is designed to investigate the dynamics of the flexible disk when rotating close to a co-rotating, a counter-rotating and a fixed rigid disk, which works as a stabilizer. The effects of rotational speed, initial gap height and inlet-hole radius on the flexible disk displacement and its vibration amplitude are investigated experimentally for the different types of stabilizer. Finally, the analytical and experimental results are compared.

• Journal of Korea Water Resources Association
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• v.36 no.4
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• pp.705-713
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• 2003

To investigate the run-up heights of nearshore tsunamis in the vicinity of a circular island, a numerical model has been developed based on quadtree grids. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using a finite difference leap-frog scheme on adaptive hierarchical quadtree grids. The quadtree grids are generated around a circular island where refined with rectangular or circular domain. Obtained numerical results have been verified by comparing to available laboratory measurements. A good agreement has been achieved.

• Journal of Korea Water Resources Association
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• v.38 no.6 s.155
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• pp.461-469
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• 2005

A second-order upwind scheme is used to investigate the run-up heights of tsunamis in the East Sea and the predicted results are compared with the field data and results of a first-order upwind scheme. In the numerical model, the governing equations solved by the finite difference scheme are the linear shallow-water equations in deep water and nonlinear shallow-water equations in shallow water. The target events are 1983 Central East Sea Tsunami and 1993 Hokkaido Nansei Oki Tsunami. The predicted results represent reasonably well the run-up heights of tsunamis in the East Sea. And, the results of simulation are used for the design of inundation map.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.3
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• pp.88-95
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• 2024

In this article, we propose an efficient and accurate adaptive time-stepping numerical method for the Black-Scholes (BS) equations. The numerical scheme used is the finite difference method (FDM). The proposed adaptive time-stepping computational scheme is based on the maximum norm of the discrete Laplacian values of option values on a discrete domain. Most numerical solvers for the BS equations require a small time step when there are large variations in the solutions. To resolve this problem, we propose an adaptive time-stepping algorithm that uses a small time step size when the maximum norm of the discrete Laplacian values on a discrete domain is large; otherwise, a larger time step size is used to speed up the computation. To demonstrate the high performance of the proposed adaptive time-stepping methodology, we conduct several computational experiments. The numerical tests confirm that the proposed adaptive time-stepping method improves both the efficiency and accuracy of computations for the BS equations.