• 한국전산유체공학회:학술대회논문집
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• 2007.10a
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• pp.249-257
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• 2007

A high resolution numerical method aimed at solving gas-liquid two-phase flow is proposed and applied to gas-liquid two-phase shock tube problem. The present method employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. By applying the homogeneous equilibrium cavitation model, the present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation and large density changes. The speed of sound for gas-liquid two-phase media is derived on the basis of thermodynamic relations and compared with that by eigenvalues. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media and some data related to computational efficiency are made. Comparisons of predicted results and exact solutions are provided and discussed.

• Computational Structural Engineering
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• v.10 no.4
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• pp.177-184
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• 1997

In this paper, numerical methods are developed for solving the elastica of simple beams with variable-arc-length subjected to a point loading. The beam model is based on Bernoulli-Euler beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to solve the governing differential equations and to compute the beam's rotation at the left end of the beams. Extensive numerical results of the elastica responses, including deflected shapes, rotations of cross-section and bending moments, are presented in non-dimensional forms. The possible maximum values of the end rotation, deflection and bending moment are determined by analyzing the numerical data obtained in this study.

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.281-293
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• 2014

We investigate long-term motions of the cable when cable has different types of periodic forcing term. Various different types of solutions are presented by using the 2nd order Runge-Kutta method under various initial conditions. There appeared to be small- and large-amplitude solutions which have different nodal structure.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.4
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• pp.365-373
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• 2011

This paper presents the dynamic response and the vibration characteristics for a rail-track supported by discrete springs and dampers. Recently, automatic conveyer system, rail-track, rack-master system demand the soundproof facilities and vibration suppression measures in order to satisfy the strict environmental standards. The equations of motions of the dynamic characteristics for a vibration suppression rail-track under a traveling mass were derived by Galerkin's mode summation method considering gravity, centrifugal force, Coriolis force, inertia force of the moving mass, transverse inertia of the rail-track. Also, numerical results were calculated by Runge-Kutta integration method. In order to investigate vibration characteristics and dynamic responses, modal testing and measurement of the responses of the rail-track were performed. Through the experiment and numerical simulations, numerical results have a good agreement with experimental ones.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.1
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• pp.572-583
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• 2019

This paper aims to assess the applicability of the Runge Kutta Discontinuous Galerkin-Direct Ghost Fluid Method to the internal explosion inside a water-filled tube, which previously was studied by many researchers in separate works. Once the explosive charge located at the inner center of the water-filled tube explodes, the tube wall is subjected to an extremely high intensity fluid loading and deformed. The deformation causes a modification of the field of fluid flow in the region near the water-structure interface so that has substantial influence on the response of the structure. To connect the structure and the fluid, valid data exchanges along the interface are essential. Classical fluid structure interaction simulations usually employ a matched meshing scheme which discretizes the fluid and structure domains using a single mesh density. The computational cost of fluid structure interaction simulations is usually governed by the structure because the size of time step may be determined by the density of structure mesh. The finer mesh density, the better solution, but more expensive computational cost. To reduce such computational cost, a non-matched meshing scheme which allows for different mesh densities is employed. The coupled numerical approach of this paper has fewer difficulties in the implementation and computation, compared to gas dynamics based approach which requires complicated analytical manipulations. It can also be applied to wider compressible, inviscid fluid flow analyses often found in underwater explosion events.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.3
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• pp.87-99
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• 1994

Reynolds Averaged Navier-Stokes equations are solved numerically for the computation of turbulent flow around a Wigley double model. A second order finite difference method is applied for the spatial discretization on the nonstaggered grid system and 4-stage Runge-Kutta scheme for the numerical integration in time. In order to increase the time step, residual averaging scheme of Jameson is adopted. Pressure field is obtained by solving the pressure-Poisson equation with the appropriate Neumann boundary condition. For the turbulence closure, 0-equation turbulence model of Baldwin-Lomax is used. Numerical computation is carried out for the Reynolds number of 4.5 million. Comparisons of the computed results with the available experimental data show good agreements for the velocity and pressure distributions.

• 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 the Korea Concrete Institute
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• v.22 no.6
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• pp.797-803
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• 2010

A dynamic analysis procedure is developed to provide a better estimation of the dynamic responses of pre-stressed concrete (PSC) box girder bridges on the Korea high speed railway. Particularly, a three dimensional numerical model including the structural interaction between high speed vehicles, bridges and railway endures to analyze accurately and evaluate with in-depth parametric studies for dynamic responses of bridge due to the high speed railway vehicles. Three dimensional frame element is used to model the PSC box girder bridges, simply supported span lengths 40 m. The high-speed railway vehicles (K-TGV) including a locomotive are used as 38-degree of freedom system. Three displacements (vertical, lateral, and longitudinal) as well as three rotational components (pitching, rolling, and yawing) are considered in the 38-degree of freedom model. The dynamic analysis by Runge-Kutta method which are able to analyze considering the dynamic impact factors are compared and contrasted. It is proposed as an empirical formula that the impact factors damaged the bridge load-carrying capacities occurs to the bride due to high-speed vehicle.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2A
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• pp.155-162
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• 2009

This paper deals with the strongest beams with the solid regular polygon cross-section, whose volumes are always held constant. The differential equation of the elastic deflection curve of such beam subjected to the concentrated and trapezoidal distributed loads are derived and solved numerically. The Runge-Kutta method and shooting method are used to integrate the differential equation and to determine the unknown initial boundary condition of the given beam. In the numerical examples, the simple beams are considered as the end constraint and also, the linear, parabolic and sinusoidal tapers are considered as the shape function of cross sectional depth. As the numerical results, the configurations, i.e. section ratios, of the strongest beams are determined by reading the section ratios from the numerical data related with the static behaviors, under which static maximum behaviors become to be minimum.