• Transactions of the Korean hydrogen and new energy society
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• v.30 no.3
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• pp.260-268
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• 2019

The pyrolysis characteristics of pulverized coal particle was numerically analyzed with the drop tube furnace. Based on the simulated gas flow field in the drop tube furnace, the particle velocity, temperature and volatile evolution were calculated with the fourth order Runge-Kutta method. The effects of changes in reactor wall temperature and particle diameter on the pyrolysis behavior of coal particle were investigated. The particle heating rate was very sensitive to the reactor wall temperature and particle size, that is, the higher wall temperature and the smaller particle size resulted in the higher heating rate and the consequent quicker volatile evolution.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.15 no.4
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• pp.380-387
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• 1986

In this study, the models for a double-diffusive thermohaline system heated from below were developed and the governing equations were established taking account of the density variation with time. The six order Runge-Kutta method was used for the solution of the simultaneous governing differential equations and the temperature and salt concentration distributions and height of each layer within the system were predicted. As the result of this study, it was found that the predicted values with the convective layer growing proportionality constant of 0.18 showed a good agreement with available experimental data. It was also found that the effect of density change with time on the temperature profile in the bottom convective layer could not be negligible.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.55.1-55.1
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• 2020

In an attempt to investigate the nonlinear dynamics such as shock, shear, and turbulence associated with ultra-relativistic jets, we develop a new relativistic hydrodynamics (RHD) code based on the weighted essentially non-oscillatory (WENO) scheme. It is a 5th-order accurate, finite-difference scheme, which has been widely used for solving hyperbolic systems of conservation equations. The code is parallelized with MPI and OpenMP. Through an extensive set of tests, the accuracy and efficiency of different WENO reconstructions, and different time discretizations are assessed. Different implementations of the equation of state (EOS) for relativistic fluid are incorporated, As the fiducial setup for simulations of ultra-relativistic jets, we adopt the EOS in Ryu et al. (2006) to treat arbitrary adiabatic index of relativistic fluid, the WENO-Z reconstructions to minimize numerical dissipation without loss of stability, and the strong stability preserving Runge-Kutta (SSPRK) method to achieve stable time stepping with large CFL numbers. In addition, the code includes a high-order flux averaging along the transverse directions for multi-dimensional problems, and the modified eigenvalues for the acoustic modes to effectively control the carbuncle instability. We find that the new code performs satisfactorily simulations of ultra-relativistic jets.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.93-114
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• 2019

In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion. We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences. The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first-order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.

• Steel and Composite Structures
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• v.26 no.4
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• pp.453-461
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• 2018

In this paper, nonlinear vibrations of the unsymmetrical laminated composite beam (LCB) on a nonlinear elastic foundation are studied. The governing equation of the problem is derived by using Galerkin method. Two different end conditions are considered: the simple-simple and the clamped-clamped one. The Hamiltonian Approach (HA) method is adopted and applied for solving of the equation of motion. The advantage of the suggested method is that it does not need any linearization of the problem and the obtained approximate solution has a high accuracy. The method is used for frequency calculation. The frequency of the nonlinear system is compared with the frequency of the linear system. The influence of the parameters of the foundation nonlinearity on the frequency of vibration is considered. The differential equation of vibration is solved also numerically. The analytical and numerical results are compared and is concluded that the difference is negligible. In the paper the new method for error estimation of the analytical solution in comparison to the exact one is developed. The method is based on comparison of the calculation energy and the exact energy of the system. For certain numerical data the accuracy of the approximate frequency of vibration is determined by applying of the suggested method of error estimation. Finally, it has been indicated that the proposed Hamiltonian Approach gives enough accurate result.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2005.05a
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• pp.43-46
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• 2005

Micro molding technology is a promising mass production technology for polymer based microstructures. Mass production technologies such as the micro injection/compression molding, hot embossing, and micro reaction molding are already in use. In the present study, we have developed a numerical analysis system to simulate three-dimensional non-isothermal cavity filling for hot embossing, with a special emphasis on the free surface capturing. Precise free surface capturing has been successfully accomplished with the level set method, which is solved by means of the Runge-Kutta discontinuous Galerkin (RKDG) method. The RKDG method turns out to be excellent from the viewpoint of both numerical stability and accuracy of volume conservation. The Stokes equations are solved by the stabilized finite element method using the equal order tri-linear interpolation function. To prevent possible numerical oscillation in temperature Held we employ the streamline upwind Petrov-Galerkin (SUPG) method. With the developed code we investigated the detailed change of free surface shape in time during the mold filling. In the filling simulation of a simple rectangular cavity with repeating protruded parts, we find out that filling patterns are significantly influenced by the geometric characteristics such as the thickness of base plate and the aspect ratio and pitch of repeating microstructures. The numerical analysis system enables us to understand the basic flow and material deformation taking place during the cavity filling stage in microstructure fabrications.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.38-52
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• 1991

In this paper, a semi-Lagrangian method is used to solve the nonlinear hydrodynamics of a three-dimensional body beneath the free surface in the time domain. The boundary value problem is solved by using the boundary integral method. The geometries of the body and the free surface are represented by the curved panels. The surfaces are discretized into the small surface elements using a bi-cubic B-spline algorithm. The boundary values of $\phi$ and $\frac{\partial{\phi}}{\partial{n}}$ are assumed to be bilinear on the subdivided surface. The singular part proportional to $\frac{1}{R}$ are subtracted off and are integrated analytically in the calculation of the induced potential by singularities. The far field flow away from the body is represented by a dipole at the origin of the coordinate system. The Runge-Kutta 4-th order algorithm is employed in the time stepping scheme. The three-dimensional form of the integral equation and the boundary conditions for the time derivative of the potential Is derived. By using these formulas, the free surface shape and the equations of motion are calculated simultaneously. The free surface shape and fille forces acting on a body oscillating sinusoidally with large amplitude are calculated and compared with published results. Nonlinear effects on a body near the free surface are investigated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.9
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• pp.879-888
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• 2012

This study aims to apply multistage homotopy perturbation method(MHPM) to space truss composed of discrete members to obtain a semi-analytical solution. For the purpose of this research, a nonlinear governing equation of the structures is formulated in consideration of geometrical nonlinearity, and homotopy equation is derived. The result of carrying out dynamic analysis on a simple model is compared to a numerical method of 4th order Runge-Kutta method(RK4), and the dynamic response by MHPM concurs with the numerical result. Besides, the displacement response and attractor in the phase space is able to delineate dynamic snapping properties under step excitations and the responses of damped system are reflected well the reduction effect of the displacement.

• Structural Engineering and Mechanics
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• v.63 no.4
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• pp.551-565
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• 2017

In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

• Journal of the Korean Society of Clothing and Textiles
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• v.29 no.9_10 s.146
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• pp.1359-1368
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• 2005

When we develop the tight-fit 2D pattern from the 3D scan data, segmentation of the 3D scan data into several parts is necessary to make a curved surface into a flat plane. In this study, Garland's method of triangle simplification was adopted to reduce the number of data point without distorting the original shape. The Runge-Kutta method was applied to make triangular patch from the 3D surface in a 2D plane. We also explored the detailed arrangement method of small 2D patches to make a tight-fit pattern for a male body. As results, minimum triangle numbers in the simplification process and efficient arrangement methods of many pieces were suggested for the optimal 2D pattern development. Among four arrangement methods, a block method is faster and easier when dealing with the triangle patches of male's upper body. Anchoring neighboring vertices of blocks to make 2D pattern was observed to be a reasonable arrangement method to get even distribution of stress in a 2D plane.