• Journal of computational fluids engineering
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• v.2 no.1
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• pp.8-12
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• 1997

The three-dimensional Euler equations are solved numerically for the analysis of contraction flows in wind or water tunnels. A second-order finite difference method is used for the spatial discretization on the nonstaggered grid system and the 4-stage Runge-Kutta scheme for the numerical integration in time. In order to speed up the convergence, the local time stepping and the implicit residual-averaging schemes are introduced. The pressure field is obtained by solving the pressure-Poisson equation with the Neumann boundary condition. For the evaluation of the present Euler solver, numerical computations are carried out for three contraction geometries, one of which was adopted in the Large Cavitation Channel for the U.S. Navy. The comparison of the computational results with the available experimental data shows good agreement.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.36-40
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• 2006

A comparative study on flux functions for the 2-dimensional Euler equations has been conducted. Explicit 4-stage Runge-Kutta method is used to integrate the equations. Flux functions used in the study are Steger-Warming's, van Leer's. Godunov's, Osher's(physical order and natural order), Roe's, HILE, AUSM, AUSM+ and AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.7 s.196
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• pp.69-74
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• 2007

The paper proposes a new sonic resonance test for a elastic modulus measurement which is based on time-average electronic speckle pattern interferometry(TA-ESPI) and Euler-Bernoulli equation. Previous measurement technique of elastic constant has the limitation of application for thin film or polymer material because contact to specimen affects the result. TA-ESPI has been developed as a non-contact optical measurement technique which can visualize resonance vibration mode shapes with whole-field. The maximum vibration amplitude at each vibration mode shape is a clue to find the resonance frequencies. The dynamic elastic constant of test material can be easily estimated from Euler-Bernoulli equation using the measured resonance frequencies. The proposed technique is able to give high accurate elastic modulus of materials through a simple experiment set up and analysis.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.116-119
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• 2007

In this study the unsteady aerodynamic analysis of a hovering helicopter rotor is performed. For the accurate flow field analysis Euler equations and the free wake method are coupled. The Euler equations are solved to find the pressure distribution around the rotor, and free wake method is used to give the boundary condition for the solution of Euler equations. Also, vortex strength and wake motion after the rotor are simulated by the free wake method. The accuracy of the present method is compared with the source sink model. The present method is applied to the hovering Caradonna-Tung rotor and compared with experimental results.

• 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.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.49-55
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• 2003

A comprehensive study has been made for the investigation of the convergence characteristics of the LU scheme for the Euler equations using von Neumann stability analysis. The stability results indicate that the convergence rate is governed by a specific parameter combination. Based on this insight it is shown that the LU scheme will not suffer convergence deterioration at any grid aspect ration if the local time step is defined using appropriate parameter combination. The numerical results demonstrate that this time step definition gives uniform convergence for grid aspect ratios from one to $1\times10^4$.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.127-136
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• 2007

In this paper, the equations of the scaled boundary finite element method are derived for non-homogeneous half plane and analyzed numerically In the scaled boundary finite element method, partial differential equations are weaken in the circumferential direction by approximation scheme such as the finite element method, and the radial direction of equations remain in analytical form. The scaled boundary equations of non-homogeneous half plane, its elastic modulus varies as power function, are newly derived by the virtual work theory. It is shown that the governing equation of this problem is the Euler-Cauchy equation, therefore, the logarithm mode used in the half plane problem is not valid in this problem. Two numerical examples are analysed for the verification and the feasibility.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.1A
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• pp.53-60
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• 2009

This paper deals with the geometrical nonlinear analyses of post-buckled columns with variable cross-section. The objective columns having variable cross-section of the width, depth and square tapers are supported by both hinged ends. By using the Bernoulli-Euler beam theory, differential equations governing the elastica of post-buckled column and their boundary conditions are derived. The solution methods of these differential equations which have two unknown parameters are developed. As the numerical results, equilibrium paths, elasticas and stress resultants of the post-buckled columns are presented. Laboratory scaled experiments were conducted for validating the theories developed in this study.

• Journal of the military operations research society of Korea
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• v.10 no.1
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• pp.15-22
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• 1984

오일러의 미분 방정식은 보조 방정식을 이용하면 쉽게 일반해를 구할 수 있다. 정의된 유사-오일러 미분 방정식을 풀기 위해 규정된 조건을 만족토록 하면 보조 방정식을 이용하여 일반해를 쉽게 구할 수 있음을 보였다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.3
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• pp.702-707
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• 2004

This article is concerned with container pose estimation using CCD a camera and a range sensor. In particular, the issues of characteristic point extraction and image noise reduction are described. The Euler-Lagrange equation for gaussian and random noise reduction is introduced. The alternating direction implicit(ADI) method for solving Euler-Lagrange equation based on partial differential equation(PDE) is applied. The vertex points as characteristic points of a container and a spreader are founded using k order curvature calculation algorithm since the golden and the bisection section algorithm can't solve the local minimum and maximum problems. The proposed algorithm in image preprocess is effective in image denoise. Furthermore, this proposed system using a camera and a range sensor is very low price since the previous system can be used without reconstruction.