• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.382-390
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• 1992

The problem of natural convection from a vertical fin is solved by coupling the thermal diffusion equation in the fin to the constitutive equations of the ambient medium involving the radiation of the medium. The analysis is accomplished by employing an integral method. The governing equations for the problem are solved by shooting method based on the Runge-Kutta Scheme at Pr= 0.7. For the range of values of the fin parameter and the radiation-conduction parameter in the analysis, the numerical results show that the radiation effects play an important role in the heat transfer and enhance the heat transfer.

• Wind and Structures
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• v.16 no.4
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• pp.323-340
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• 2013

An active mass damper system for flutter control of bridges is presented. Flutter stability of bridge structures is improved with the help of eccentric rotational actuators (ERA). By using a bridge girder model that moves in two degrees of freedom and is subjected to wind, the equations of motion of the controlled structure equipped with ERA are established. In order to take structural nonlinearities into consideration, flutter analysis is carried out by numerical simulation scheme based on a 4th-order Runge-Kutta algorithm. An example demonstrates the performance and efficiency of the proposed device. In comparison with known active mass dampers for flutter control, the movable eccentric mass damper and the rotational mass damper, the power demand is significantly reduced. This is of advantage for an implementation of the proposed device in real bridge girders. A preliminary design of a realization of ERA in a bridge girder is presented.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.90-92
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• 1993

Stability analysis is an essential work in the operation and planning of power system. There are two categories, direct method and indirect method, and indirect method calculates the trajectories of states by numerical methods. Popular method using explicit integration has relatively low accuracy, so a more accurate method is requested. By the consideration of bus voltage variation, Runge-Kutta 4th order method can be made more accurate, but this scheme need much computation time. Through three recipes, computational cost of proposed method can be reduced. So the proposed method has improved accuracy and slight rise in cost. the method was tested on the IEEE 14 bus system.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.597-601
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• 2008

Three-dimensional structures of detonation wave propagating in circular tube were investigated. Inviscid fluid dynamics equations coupled with a conservation equation of reaction progress variable were analyzed by a MUSCL-type TVD scheme and four stage Runge-Kutta time integration. Variable-$\gamma$ formulation was used to account for the variable properties between unburned and burned states and the chemical reaction was modeled by using a simplified one-step irreversible kinetics model. The computational code was parallelized based on domain decomposition technique using MPI-II message passing library. The computations were carried out using a home made Windows based PC cluster having 160 AMD AthloxXP and Athlon64 processor. The computational domain consisted of through a roundshaped tube with wall conditions. As an initial condition, analytical ZND solution was distributed over the computational domain with disturbances. The disturbances has circumferential large gradient. The unsteady computational results in three-dimension show the detailed mechanisms of multi-cell mode of detonation wave instabilities resulting diamond shape in smoked-foil record.

• Nuclear Engineering and Technology
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• v.51 no.6
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• pp.1650-1657
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• 2019

Fluidelastic instability and nonlinear dynamics of tube bundles is a key issue in a steam generator. Especially, once the post-instability motion of the tube becomes larger than the clearance gap to other tubes, effective contact or impact between the tubes under consideration and the other tube inevitable. There is seldom theoretical analysis to the nonlinear dynamic characteristics of a tube array in two-phase flow. In this paper, experimental and numerical studies were utilized to obtain the critical velocity of the flow-induced instability of a rotated triangular tube array. The calculation results agreed well with the experimental data. To explore the post-instability dynamics of the tube array system, a Runge-Kutta scheme was used to solve the nonlinear governing equations of tube motion. The numerical results indicated that, when the flow pitch velocity is larger than the critical velocity, the tube array system is undergoing a limit cycle motion, and the dynamic characteristics of the tube array are almost similar for different void fractions.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.753-765
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• 2020

Smoking is one of the main causes of health problems and continues to be one of the world's most significant health challenges. In this paper, we use the multi-step Adomian decomposition method (MSADM) to obtain approximate analytical solutions for a mathematical fractional model of the evolution of the smoking habit. The proposed MSADM scheme is only a simple modification of the Adomian decomposition method (ADM), in which ADM is treated algorithmically with a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically. The results reveal that the method is effective and convenient for solving linear and nonlinear differential equations of fractional order.

• Steel and Composite Structures
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• v.38 no.1
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• pp.33-45
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• 2021

The Runge-Kutta method of 6th-order has been employed in this paper to analyze the flow of Casson nanofluid along permeable exponentially stretching cylinder. The modeled PDEs are changed into nonlinear ODEs through appropriate nonlinear transformations. The aim of the paper is to investigate the effects of different parameters such as Casson fluid parameter, slip parameter, suction parameter, Prandtl number, Lewis number, Brownian motion parameter, and thermophoresis parameter, with the variation of mass concentration profile. Numerical results are attained using a renowned numerical scheme shooting technique and for the authenticity of present methodlogy, the results are verified with earlier open text.

• Computers and Concrete
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• v.30 no.5
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• pp.369-375
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• 2022

Current exertion reports the numerical analysis of boundary layer slip flow of Casson Nano fluid along a permeable cylinder that is stretching in exponential manner. The modeled PDEs are changed into nonlinear ODEs through appropriate nonlinear transformations. Numerical results are attained using a renowned numerical scheme shooting method with Runge-Kutta procedure of 6^th-order. Influential role of relevant parameters like Reynolds, suction, Casson fluid and slip parameters on velocity profile is investigated. The effect of influence of slip parameter γ on temperature profile is seen through graph. To ensure the authenticity of numerical procedure, outcomes of some special cases of present work are compared with published work and strong agreement is noticed.

• Journal of computational fluids engineering
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• v.9 no.1
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• pp.1-9
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• 2004

Large eddy simulation is used to investigate the compressible flow over a cavity with high aspect ratio. The sub-grid scale stresses are modeled using the dynamic model. The compressible Navier-Stokes equations are solved with the sixth order accurate compact finite difference scheme in the space and the 4th order Runge-Kutta scheme in the time. The buffer Bone techniques are used for non-reflecting boundary conditions. The results show the shear layer oscillation over the cavity. The votical disturbances, the roll-up of vorticity, and impingement and scattering of vorticity at the downstream cavity edge can be seen in the shear layer. Several peaks for the resonant frequencies are found in the spectra of the vertical velocity at the center-line. The most energetic Peak near the downstream edge is different from that at the center part of the cavity The pressure has its minimum value in the vortex core inside the cavity, and becomes very high at the downstream face of the cavity. The variation of the model coefficient predicted by the dynamic model is quite large between 0 and 0.3. The model coefficient increases in the stream-wise evolution of the shear layer and sharply decreases near the wall due to the wall effect.

• Journal of the Korean earth science society
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• v.39 no.4
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• pp.317-326
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• 2018

Effect of the nonuniform grid on the two-dimensional transport equation was investigated in terms of theoretical analysis and finite difference method (FDM). The nonuniform grid having a typical structure of the numerical weather forecast model was incorporated in the vertical direction, while the uniform grid was used in the zonal direction. The staggered and non-staggered grid were placed in the vertical and zonal direction, respectively. Time stepping was performed with the third-order Runge Kutta scheme. An error analysis of the spatial discretization on the nonuniform grid was carried out, which indicated that the combined effect of the nonuniform grid and advection velocity produced either numerical diffusion or numerical adverse-diffusion. An analytic function is used for the quantitative evaluation of the errors associated with the discretized transport equation. Numerical experiments with the non-uniformity of vertical grid were found to support the analysis.