• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.813-829
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• 2011

In this article, we present a numerical scheme for solving singularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and boundary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence of perturbation parameter and nonlinearity in the problem leads to severe difficulties in the solution approximation. To overcome such difficulties the present numerical scheme is constructed. In construction of the numerical scheme, the first step is the dicretization of the time variable using forward difference formula with constant step length. Then, the resulting non linear singularly perturbed semidiscrete problem is linearized using quasi-linearization process. Finally, differential quadrature method is used for space discretization. The error estimate and convergence of the numerical scheme is discussed. A set of numerical experiment is carried out in support of the developed scheme.

• Journal of Ship and Ocean Technology
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• v.5 no.4
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• pp.29-43
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• 2001

In this paper, free surface flows around an advancing two-dimensional rectangular cylinder piercing the free surface are studied using numerical and experimental methods. Especially, wave breaking phenomenon around the cylinder is treated in detail. A series of numerical simulations and experiments were performed for the purpose of comparison. For the numerical simulations, a finite difference method was adopted with a rectangular grid system, and the variation of the free surface was computed by the marker density method. The computational results are compared with the experiments. It is confirmed that the present numerical method is useful for the numerical simulation of nonlinear free surface waves around a piercing body.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.207-217
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• 1991

• Tunnel and Underground Space
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• v.21 no.2
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• pp.128-137
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• 2011

The shut-in pressure calculated in common hydrofracturing test for vertical borehole equals generally to the minimum horizontal principal stress, so it should be considered as an essential parameter for determining the in-situ stress regime around the rock mass. It shows usually an ambiguous value in pressure-time history curves, however, because of the relationship between the behavior of hydraulic fractures and the condition of remote stress regime. In this study, a series of numerical analyses have been carried out to compare several methods for determining the shut-in pressure during hydrofracturing. The hydraulic-mechanical coupling has been applied to numerical analysis for simulating the fracture propagation by hydraulic pressure, and the different discontinuity geometry has been considered in numerical models to examine the effect of numerical element shape on fracture propagation pattern. From the numerical simulations with the four different discontinuity geometries, it was revealed that the shut-in pressure obtained from graphical methods rather than statistical method was relatively small. Consequently a care should be taken in selecting a method for determining the shut-in pressure when a stress anomaly around borehole and a fracture propagation with complicate mechanism are considered.

• 한국전산유체공학회:학술대회논문집
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• 2000.10a
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• pp.9-14
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• 2000

Computational methods can be classified roughly into two parts: one is the methods based on a potential flow theory, and the other is numerical solvers(CFD) based on Navier-Stockes equation. Methods based on a potential theory are more effective than CFD when the free surface effect is considered. Especially Rankine source method seems to become widespread for simulations of wave making problems. For computations of viscous flow problems, CFD techniques have rapidly been developed and have shown many successful results in the viscous flow calculation. Present paper introduces a computational system 'WAVIS' which includes a pre-processor, potential ant viscous flow solvers and a post-processor. To validate the system, the calculated results for modem commercial hull forms are compared with measurements. It is found that the results from the system are in good agreement with the experimental data, illustrating the accuracy of the numerical methods employed for WAVIS.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.2
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• pp.202-212
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• 1997

In this study, performance of the multi-stage explicit methods for numerical computation of the unsteady Navier-Stokes equations is investigated. Three methods under consideration are 1 st-, 2 nd-, and 4 th-order Runge-Kutta (R-K) methods. Compared in this estimation is stability, accuracy, and CPU time of each method. The computational codes developed are applied to the two-dimensional flow in a square cavity driven by an oscillating lid. It turned out that at Reynolds number 400, the 1 st-order R-K method is the best, while at 3200 the 2 nd-order R-K is recommended. At higher Reynolds numbers, it is conjectured that the 4 th-order R-K method will be the best algorithm among three due to its highest stability.

• Korea-Australia Rheology Journal
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• v.18 no.2
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• pp.91-98
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• 2006

We compare FT (Fourier Transform) and SD (Stress Decomposition), the interpretation methods for LAOS (Large Amplitude Oscillatory Shear). Although the two methods are equivalent in mathematics. they are significantly different in numerical procedures. Precision of FT greatly depends on sampling rate and length of data because FT of experimental data is the discrete version of Fourier integral theorem. FT inevitably involves unnecessary frequencies which must not appear in LAOS. On the other hand, SD is free from the problems from which FT suffers, because SD involves only odd harmonics of primary frequency. SD is based on two axioms on shear stress: [1] shear stress is a sufficiently smooth function of strain and its time derivatives; [2] shear stress satisfies macroscopic time-reversal symmetry. In this paper, we compared numerical aspects of the two interpretation methods for LAOS.

• KIEAE Journal
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• v.10 no.4
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• pp.3-8
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• 2010

Recently, various daylight evaluation methods for visual environment have been developed; simulation analysis methods, numerical calculation, and data monitoring methods. However, it is impossible for simulation analysis to make real scenes and visualize real images exactly. Also, a numerical calculation is considered as an out of date and time-consuming mean. Therefore, for acquisition of accurate results, many studies often use the monitoring data methods. Especially, most studies regarding discomfort glare are evaluated by measuring the physical quantity of luminance through traditional measuring Minolta Luminance meters as an instrument. But, this method has a difficulty in measuring several points at the same time because of the limitation of spaces and time when mapping. So, this study focused on the potential usefulness of High Dynamic Range photography technique as a luminance mapping tool. In order to evaluate the accuracy of proposed programs such as webHDR, Photomatix and PHOTOLUX, this paper has conducted an experiment by using Canon EOS 5D and NICON Coolpix8400 digital camera.