• Journal of computational fluids engineering
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• v.12 no.1
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• pp.43-52
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• 2007

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, HLLE, AUSM, AUSM+, AUSMPW+ and M-AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

• 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 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 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 the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.27-37
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• 1991

In this paper the nonlinear free surface flows for an axisymmetric submerged body oscillating beneath the free surface are solved and the forces acting on the body are calculated. A boundary integral method is applied to solve the axisymmetric boundary value problem and the Runge-Kutta 4-th order method is used for the time stepping of the free surface location. The nonlinear forces acting on the axisymmetric body are computed and compared with published results.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.1
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• pp.82-88
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• 2008

In this paper, Runge-Kutta (RK)-Butcher algorithm is proposed to study the periodic and oscillatory problems. Simulation results obtained using RK-Butcher algorithms and the classical fourth order Runge-Kutta (RK(4)) methods are compared with the exact solutions of a few periodic and oscillatory problems to confirm the performance of the proposed algorithm. The simulation results from RK-Butcher algorithms are always found to be very close to the exact solutions of these problems. Further, it is found that the RK-Butcher algorithm is superior when compared to RK(4) methods in terms of accuracy. The RK-Butcher algorithm can be easily implemented in a programming language and a more accurate solution may be obtained for any length of time. RK-Butcher algorithm is applicable as a good numerical algorithm for studying the problems of orbit and two body as it gives the nearly identical solutions.

• Applied Chemistry for Engineering
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• v.9 no.7
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• pp.1079-1084
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• 1998

Reaction kinetics between 4,4'-dihexyl methane diisocyanate($H_{12}MDI$) and n-hexanol in toluene with dibutyltin dilaurate(DBTDL) as catalyst was studied by experimental measurements and mathematical modeling. Experiments were carried out at various temperatures, catalyst concentrations and [NCO]/[OH] ratios, and the reaction kinetics were described by two second-order reactions, the one between NCO and OH leading to urethane and the other between urethane and NCO leading to allophanate. The rate constants were estimated by the Runge-Kutta 4th-order method. Experiments and mathematical simulations showed a good agreement for various experimental conditions. The [allophanate]/[urethane] ratios at 90% conversion of initial NCO were estimated to be over 20% for most conditions employed in the present study, indicating that allophanate formation might significantly affect the properties of urethane polymers.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.2
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• pp.101-107
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• 2012

In this study, Constraint Force Equation Methodology (CFEM) is used to develop a multi-body dynamic analysis program with constraints. Seven constraint models are implemented to analyze constraint motions of multiple bodies. The augmented equations with the constraints are solved with the 4th order Runge-Kutta method for higher degree of accuracy. The analysis code is verified by comparing the analysis results of the motion of bodies with various constraints to published results.

• Journal of Advanced Marine Engineering and Technology
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• v.23 no.6
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• pp.794-805
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• 1999

Pneumatic cushioning cylinders are commonly employed for vibration and shock control. A mathematical simulation model of a double acting pneumatic cushioning cylinder designed to absorb shock loads is presented which is based on the following assumptions; ideal equation of state isentropic flow through a port conservation of mass polytropic thermodynamics single degree of freedom piston dynamics and energy equivalent linear damping. These differential equation can be solved through numerical integration using the fourth order Runge-Kutta method. An experimental study was conducted to validate the results obtained by the numerical integra-tion technique. Simulated results show good agreement with experimental data. The computer simulation model presented here has been extremely useful not only in understanding the has been extremely useful not only in understanding the basic cushioning but also in evaluating different designs.

• Journal of Biomedical Engineering Research
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• v.24 no.4
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• pp.329-337
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• 2003

Blood in congenital or acquired AY fistula(arteriovenous fistula) flows from arteries directly to veins. detouring peripheral micro-circulation. This makes a great effect on the hemodynamics of human cardiovascular system. In this study, a computational method using lumped parameter mode) was proposed to simulate the cardiovascular hemodynamics of patients with acute AV fistula The cardiovascular system model with a fistula compartment in left lower limb was built using 17 standard lumped compartments. Using fourth order Runge-Kutta method. we solved numerically the unsteady linear set of the ordinary differential equations resulting from application of Kirchhoff's law to the lumped parameter hemodynamic model. The baroreceptor reflex system was implemented to explain the auto-regulation effect of the cardiovascular system with acute AV fistula.