• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.2
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• pp.95-101
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• 2017

In this study, we derived theoretical equations for the zigzag movement of a leading vehicle, which is the most frequent behavior in train accidents, by using a simplified spring-mass model for the rolling stock. In order to solve the equations of motion, we applied the Runge-Kutta method, which is the typical numerical analysis method used for differential equations. Furthermore, the lateral displacement of the wheel-set at the wheel-rail interface was estimated using kinetic energy. In order to verify the derived equations, we compared the theoretical and simulated results under various collision conditions. The maximum relative deviations of the lateral displacements were 0.8 [%] ~ 4.7 [%] in light collisions and 0.6 [%] ~ 5.1 [%] under derailment conditions. When an accident is simulated, these theoretical equations can be used to predict the overall behavior and obtain the offset of the body-to-body link as the initial perturbation.

• Bulletin of the Society of Naval Architects of Korea
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• v.26 no.3
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• pp.41-50
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• 1989

A basic formulation of the panel method, which is based on the potential field formulation, is reviewed for the case of two-dimensional hydrofoil problems. Numerical procedures to improve the computational efficiency of the panel method are suggested. By investigating local behavior of the flow around the trailing edge, a wedge type Kutta condition is formulated. By subdividing the trailing edge panels, where dipole strengths of the subdivided panels follow the local behavior of the potential values of the flow outside a wedge, the circulation around a hydrofoil is calculated accurately with a relatively small number of panels. The subdividing technique to improve the accuracy of the numerical Kutta condition is proved to be efficient. A local behavior of the flow around the leading edge is also investigated. By matching the flow around the leading edge with that around a parabola, a very accurate velocity distribution is obtained with relatively small number of panels. An accurate prediction of the stagnation point and the pressure distribution near the leading edge may contribute to improve the accuracy of cavity predictions and boundary layer calculations around hydrofoils.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.4
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• pp.981-989
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• 1990

본 연구에서는 유한체적법에 의한 4단계 Runge-Kutta방법으로 2차원 익열에 대한 비점성 천음속 유동장에 대한 해석을 수행하기로 하는데 이는 경계층방정식에 대 한 경계조건으로 이용될 수 있고 3차원 계산시 그 기초자료가 될 수 있을 것이다.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.28 no.6
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• pp.573-578
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• 2010

Precise determination of satellite positions is necessary to improve positioning accuracy in GNSS. In this study, GLONASS orbits were predicted from broadcast ephemeris using the 4th-order Runge-Kutta numerical integration method and their accuracy dependence on the integration step and the integration time was analyzed. The 3D RMS (Root Mean Square) differences between the results from I-second integration step and 300-second integration step was about 3 cm, but the processing time was one hundred times less for the I-second integration time case. For trials of different integration times, the 3D RMS errors were 8.3 m, 187.3 m, and 661.5 m for 30-, 150-, and 300-minutes of integration time, respectively. Though this integration-time analysis, we concluded that the accuracy gets higher with a shorter integration time. Thus we suggest forward and backward integration methods to improve GLONASS positioning accuracy, and with this method we can achieve a 5-meter level of 3-D orbit accuracy.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.2
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• pp.107-115
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• 1999

In order to develop a convenient method for the estimation of transport distance of settling stones in quiescent water or flowing water, introduced was the simple but relatively accurate equation of drag coefficient. The equation of drag coefficient introduced was confirmed to give relatively accurate evaluation for the drag force of smooth-surface sphere, and the effects of surface roughness and shape can be considered by adjusting empirical parameters. A theoretical equation has been developed for the settling velocity or settling distance of smooth-surface sphere in quiescent fluid, and the computation results have been obtained by adjusting the empirical parameter for the settling distance of stone in quiescent water. The 2nd order ordinary differential equation has been developed for the case of settling stones in flowing fluid, and a numerical model has been developed by using Runge-Kutta method for its solution. A number of cases have been tested by adjusting the empirical parameter.

• Journal of the Korean Society of Propulsion Engineers
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• v.10 no.2
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• pp.1-14
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• 2006

Present study examines the numerical issues of cell structure simulation for various regimes of detonation phenomena ranging from weakly unstable to highly unstable detonations. Inviscid fluid dynamics equations with $variable-{\gamma} $ formulation and one-step Arrhenius reaction model are solved by a MUSCL-type TVD scheme and 4th order accurate Runge-Kutta time integration scheme. A series of numerical studies are carried out for the different regimes of the detonation phenomena to investigate the computational requirements for the simulation of the detonation wave cell structure by varying the reaction constants and grid resolutions. The computational results are investigated by comparing the solution of steady ZND structure to draw out the minimum grid resolutions and the size of the computational domain for the capturing cell structures of the different regimes of the detonation phenomena.

• Journal of Astronomy and Space Sciences
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• v.5 no.1
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• pp.19-30
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• 1988

The existence of the j-type collision periodic orbit is examined on the condition of mass ratio 0.9878449 and Jacobian constant 2.9∼3.4. Using the Birckhoff's regularization method and the 5th order Runge-Kutta variable step-sized numerical roution introduced by Fehlberg (1968). we test their periodicities. As the results, 4 j-type collision orbits and 5 peculiar orbits are represented. There are good agreements in this collision orbits with the relationship between the period and the shape of orbit proposed by Pinotsis Zikides(1984).

• Journal of Advanced Marine Engineering and Technology
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• v.17 no.2
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• pp.44-51
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• 1993

Here is represented a vortex panel method to evaluate the performance characteristics of the 2-dimensional turbomachinery with circular arc blades or logarithmic blades. The present method is characterized by distributing small consecutive panels of linearly varing vortex strength satisfying boundary condition at control points and Kutta condition at trailing edge. To confirm the reliability of the present method, experimental result of a 2-D pump impeller of six circular arc blades is compared with the calculated one. As an application of the present method, figures are presented in series showing velocity and pressure distribution between blades.

• Journal of Ocean Engineering and Technology
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• v.2 no.1
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• pp.83-89
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• 1988

정지된 유동장에 놓인 반무한 평판이 횡방향으로 갑자기 출발하는 경우에 있어서 평판의 끝에서 발생하는 보텍스의 거동을 해석적 및 수치적 측면에서 검토하였다. 해석적 방법은 단일 보텍스 모델에 근거를 두었으며, 해석결과 순환량은 시간의 1/3승, 보텍스의 중심까지의 거리는 시간의 2/3승에 비례하여 증가함을 알 수 있었다. 룬게.쿠타(Runge-Kutta)방법을 써서 분리 보텍스 모델에 따른 비선형 운동방정식의 해를 수치적으로 구했다. 수치해는 시간의 경과에 따라 해석 해에 접근하였다. 보텍스의 형상에 있어서도 실험결과와 잘 맞았다.

• Journal of the Society of Naval Architects of Korea
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• v.38 no.1
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• pp.1-8
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• 2001

The computations of the turbulent flow around the ship models with the free-surface effects were carried out. Incompressible Reynolds-Averaged Navier-Stokes equations were solved by using an explicit finite-difference method with the nonstaggered grid system. The method employed second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration. For the turbulence closure, a modified Baldwin-Lomax model was exploited. The location of the free surface was determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and a free-surface conforming grid was generated at each time step so that one of the grid boundary surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition was applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method developed in the present study, the computations were carried out for beth Wigley and Series 60 $C_B=0.6$ ship model and the computational results showed good agreements with the experimental data.