• Water for future
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• v.29 no.5
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• pp.173-184
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• 1996

In this study, a two-dimensional shallow-water equation was used to develop the mathematical model for computing water levels and flow distribution. In the discretization equations, based on the finite volume method (FVM), the third order Runge-Kutta method and the third order upwind scheme were introduced to handle the unsteady and vconvective terms in the governing equations. To determine the accuracy of the developed model, it was applied to the rectangular horizontal channel in a frictionless flow. The water depth and velocity obtained by the numerical model were found to agree closely with the exact solution. The model was also applied to the rectangular channel with both the symmetric and the non symmetric constriction. The velocity distribution of the flow and the propagation of the flood wave were simulated and the results well described the flow characteristics.

• Water for future
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• v.29 no.5
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• pp.235-244
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• 1996

A one-dimensional eddy diffusion model and a mixed-layer model are developed and applied to simulate the vertical temperature profiles in lakes. Also the running results of each method are compared and analyzed. In an eddy diffusion model, molecular diffusivity is neglected and eddy diffusivity which does not need lake-specific fitting parameter and constant lake's level are applied. The heat exchanges at the water surface and the bottom are formulated by the energy balance and zero energy gradient, respectively. In a mixed-layer model, two layers approach which has a constant thickness is adopted. Application of these models which use explicit finite difference an Runge-Kutta methods respectively demonstrates that the models efficiently simulate water temperatures.

• Tribology and Lubricants
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• v.33 no.6
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• pp.309-314
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• 2017

This paper presents a theoretical investigation of the dynamic characteristics of externally pressurized air pad bearings with closed loop grooves. These grooves are made on the surface of bearings to reduce the number of supply holes so that manufacturing costs can be reduced. The semi-implicit method is applied to calculate the time varying pressure profile on the air bearing surface owing to the advantages of numerical stability and fast time tracing characteristics. The static pressure of the groove bearings is much higher than that without grooves, so the groove bearings can provide high load carrying capacity. The equation of motion considering vertical motion and tilting motion are also solved using the Runge-Kutta 4th order method. By combining the semi-implicit method and the Runge-Kutta method, fast calculations of the dynamic behavior of the air bearing can be achieved. The variations of bearing reaction force, air film reaction moment, height, and tilting angle are investigated for the step force input, which is 20% higher than the bearing reaction, when the nominal clearance is 6 mm. The effect of the groove width and the groove depth are investigated by calculating the dynamic behavior. The possibility of the air hammering with the depth of the groove is found and discussed.

• Journal of the Korean Magnetics Society
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• v.2 no.1
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• pp.69-74
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• 1992

This paper describes the energy and speed characteristics of an induction coil-gun. The coil-gun has some merits that it can be easily installed and repeatedly used many times, it does not damage mechanically in the course of launch and the force exerted on the projectile is distributed uniformly. An equivalent circuit is employed for modeling the coil-gun. The circuit equations and equation of motion are then derived based on the equivalent circuit. These equations are solved numerically by using Runge-Kutta method. Finally the energy transfer ratios are obtained according to the variations of the resonant frequency of driving circuit and charging voltage of capacitors. The muzzle velocities of projectile are also obtained according to the variations of electrical conductivity and initial position of projectile, firing angle of driving circuit, charging voltage of capacitor and resistance of driving coil, respectively.

• Journal of Astronomy and Space Sciences
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• v.26 no.2
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• pp.199-210
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• 2009

Even though there are several Global Navigation Satellite Systems under development, only GPS and GLONASS are currently available for satellite positioning. In this study, GLONASS orbits were predicted from broadcast ephemeris using the 4th-order Runge-Kutta numerical integration. For accuracy validation, predicted orbits were compared with precise ephemeris. The RMS(Root Mean Square) and maximum 3-D errors were 14.3 km and 17.4 km for one-day predictions. In case of 7-day predictions, the RMS and maximum 3-D errors were 15.7 and 40.1 km, respectively. Also, the GLONASS satellite visibility predictions were compared with real observations, and they agree perfectly except for several epochs when the satellite signal was blocked by nearby buildings.

• Nuclear Engineering and Technology
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• v.17 no.1
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• pp.16-24
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• 1985

A computer model is developed capable of simulating the transient behavior of a pool-type liquid metal-cooled fast breeder reactor (LMFBR). The model, SIMFARP, is a fast running computer code which may be used to simulate the loss of power to any pump(s), a complete loss-of-forced cooling, and the natural circulation behavior. Eight governing equations are derived and a Runge-Kutta algorithm is applied to integrate the eight differential equations. The developed computer program is applied to two cases; loss of electric power to any pump(s), and loss of all external electric supply power without scram in Super-Phenix-I.

• Journal of Digital Contents Society
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• v.16 no.4
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• pp.575-581
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• 2015

This paper presents the development of certain highly efficient and accurate method for computing tangent curves for three-dimensional vector fields. Unlike conventional methods, such as Runge-Kutta method, for computing tangent curves which produce only approximations, the method developed herein produces exact values on the tangent curves based upon piecewise linear variation over a tetrahedral domain in 3D. This new method assumes that the vector field is piecewise linearly defined over a tetrahedron in 3D domain. It is also required to decompose the hexahedral cell into five or six tetrahedral cells for three-dimensional vector fields. The critical points can be easily found by solving a simple linear system for each tetrahedron. This method is to find exit points by producing a sequence of points on the curve with the computation of each subsequent point based on the previous. Because points on the tangent curves are calculated by the explicit solution for each tetrahedron, this new method provides correct topology in visualizing 3D vector fields.

• Journal of Korea Multimedia Society
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• v.12 no.11
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• pp.1623-1628
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• 2009

This paper presents the development of certain highly efficient and accurate method for computing tangent curves for two-dimensional vector fields. Unlike convention methods, such as Runge-Kutta, for computing tangent curves which produce only approximations, the method developed herein produces exact values on the tangent curves based on piecewise linear variation over a triangle in 2D. This new method assumes that the vector field is piecewise linearly defined over a triangle in 2D. It is also required to decompose the rectangular cell into two triangular cells. The critical points can be easily found by solving a simple linear system for each triangle. This method is to find exit points by producing a sequence of points on the curve with the computation of each subsequent point based on the previous. Because points on the tangent curves are calculated by the explicit solution for each triangle, this new method provides correct topologies in visualizing 2D vector fields.

• 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 Astronomy and Space Sciences
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• v.14 no.1
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• pp.136-141
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• 1997

To calculate the position and velocity of the artificial satellite precisely, one has to build a mathematical model concerning the perturbations by understanding and analysing the space environment correctly and then quantifying. Due to these space environment model, the total acceleration of the artificial satellite can be expressed as the 2nd order differential equation and we build an orbit propagation algorithm by integrating twice this equation by using the Cowell's method which gives the position and velocity of the artificial satellite at any given time. Perturbations important for the orbits of geostationary spacecraft are the Earth's gravitational potential, the gravitational influences of the sun and moon, and the solar radiation pressure. For precise orbit propagation in Cowell' method, 40 x 40 spherical harmonic coefficients can be applied and the JPL DE403 ephemeris files were used to generate the range from earth to sun and moon and 8th order Runge-Kutta single step method with variable step-size control is used to integrate the the orbit propagation equations.