• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.679-702
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• 2014

Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.1
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• pp.46-55
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• 2004

Thermal characteristics of the various cooling methods in electronic equipment are studied numerically. A common chip cooling system is modeled as a parallel channel with protruding heat sources. A two-dimensional model has been developed for the numerical analysis of compressible. viscous. laminar flow. and conjugate heat transfer between parallel plates with uniform block heat sources. The finite volume method is used to solve this problem. The assembly consists of two channels formed by two covers and one printed circuit board that is assumed to have three uniform heat source blocks. Various cooling methods are considered to find out the efficient cooling method in a given geometry and heat sources. The velocity and the temperature fields. the local temperature distribution along the surface of blocks. and the maximum temperature in each block are obtained. The results are compared to examine the thermal characteristics of the different cooling methods both quantitatively and qualitatively.

• Journal of The Korean Astronomical Society
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• v.34 no.4
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• pp.191-201
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• 2001

My contribution to these proceedings summarizes a general overview on High Resolution Shock Capturing methods (HRSC) in the field of relativistic hydrodynamics with special emphasis on Riemann solvers. HRSC techniques achieve highly accurate numerical approximations (formally second order or better) in smooth regions of the flow, and capture the motion of unresolved steep gradients without creating spurious oscillations. In the first part I will show how these techniques have been extended to relativistic hydrodynamics, making it possible to explore some challenging astrophysical scenarios. I will review recent literature concerning the main properties of different special relativistic Riemann solvers, and discuss several 1D and 2D test problems which are commonly used to evaluate the performance of numerical methods in relativistic hydrodynamics. In the second part I will illustrate the use of HRSC methods in several astrophysical applications where special and general relativistic hydrodynamical processes play a crucial role.

• The Mathematical Education
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• v.37 no.1
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• pp.101-114
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• 1998

In this thesis, We tried to introduce definite integration to the curriculum of high school mathematics with numerical integration, which had been introduced with quadrature method. For this purpose, We used new experimental mathematics approaches, so-called investigation and examination. In chapter II, We examined how much computers had been used in teaching mathematics. In chapter III, We presented the theoretical background of approximation integration within numerical integration. In chapter IV, We studied and compared various methods of numerical integration, and examined the relation between curvature of a curved line and numerical integration. In order to study more easily, We used some of computer programs. We hope that this thesis will be a turning point in developing new teaching methods and improving curriculum of mathematics in high school.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.513-520
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• 2014

We study numerical methods to obtain the stationary probabilities of continuous-time Markov chains whose embedded chains are periodic. The power method is applied to the balance equations of the periodic embedded Markov chains. The power method can have the convergence speed of exponential rate that is ambiguous in its application to original continuous-time Markov chains since the embedded chains are discrete-time processes. An illustrative example is presented to investigate the numerical iteration of this paper. A numerical study shows that a rapid and stable solution for stationary probabilities can be achieved regardless of periodicity and initial conditions.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.207-216
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• 2023

Three time-discontinuous Galerkin quadrature element methods (TDGQEMs) are developed for structural dynamic problems. The weak-form time-discontinuous Galerkin (TDG) statements, which are capable of capturing possible displacement and/or velocity discontinuities, are employed to formulate the three types of quadrature elements, i.e., single-field, single-field/least-squares and two-field. Gauss-Lobatto quadrature rule and the differential quadrature analog are used to turn the weak-form TDG statements into a system of algebraic equations. The stability, accuracy and numerical dissipation and dispersion properties of the formulated elements are examined. It is found that all the elements are unconditionally stable, the order of accuracy is equal to two times the element order minus one or two times the element order, and the high-order elements possess desired high numerical dissipation in the high-frequency domain and low numerical dissipation and dispersion in the low-frequency domain. Three fundamental numerical examples are investigated to demonstrate the effectiveness and high accuracy of the elements, as compared with the commonly used time integration schemes.

• Journal of Industrial Technology
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• v.43 no.1
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• pp.33-41
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• 2023

This paper provides a general overview of surface catalytic recombination in hypersonic flow. The surface catalytic recombination phenomena is elaborated in terms of its general overview and numerical modeling associated with it. The general overview of the surface catalytic recombination phenomena describes the elementary surface reactions for the surface catalytic and the role of the surface catalytic recombination efficiency in the heat transfer determination. In the numerical modeling, the surface catalytic recombination is described based on the stagnation-point boundary layer analysis, and finite-rate surface reaction modeling. Throughout this overview manuscript, a general understanding of this phenomena is obtained and can be used as foundation for deeper application with the numerical computational fluid dynamics (CFD) flow solver to estimate the surface heat transfer in the hypersonic vehicles.

• Progress in Superconductivity and Cryogenics
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• v.20 no.4
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• pp.16-19
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• 2018

This paper presents analytical and numerical simulation approaches on charging characteristics of no-insulation (NI) REBCO pancake coil by using the equivalent circuit model to estimate magnetic performance response in the coil. The analytical methods provide closed form or definite solution in the form of complete mathematical expressions but they are hard to solve the complex problems. Numerical methods have become popular with the development of the computing capabilities to solve the problems which are impossible or very hard to solve analytically. First of all, the equivalent circuit model are proposed to develop the simulation code for both analytical and numerical method. The charging test was performed under critical current to obtain magnetic field induced and terminal voltage through the radial as well as spiral current paths within the coil. To verify the validity of both proposed methods, the simulation results were compared and discussed with the experimental results.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.20 no.4
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• pp.429-453
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• 2022

Numerical modeling and scenario composition are needed to characterize the geological environment of the disposal site and analyze the long-term evolution of natural barriers. In this study, processes and features of the hydro-mechanical behavior of natural barriers were categorized and represented using the interrelation matrix proposed by SKB and Posiva. A hydro-mechanical coupled model was evaluated for analyzing stress field changes and fracture zone re-activation. The processes corresponding to long-term evolution and the hydro-mechanical mechanisms that may accompany critical processes were identified. Consequently, practical numerical methods could be considered for these geological engineering issues. A case study using a numerical method for the stability analysis of an underground disposal system was performed. Critical stress distribution regime problems were analyzed numerically by considering the strata's movement. Another case focused on the equivalent continuum domain composition under the upscaling process in fractured rocks. Numerical methods and case studies were reviewed, confirming that an appropriate and optimized modeling technique is essential for studying the stress state and geological history of the Korean Peninsula. Considering the environments of potential disposal sites in Korea, selecting the optimal application method that effectively simulates fractured rocks should be prioritized.

• International Union of Geodesy and Geophysics Korean Journal of Geophysical Research
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• v.26 no.1
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• pp.1-14
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• 1998

Various numerical methods for the two dimensional shallow water equations have been applied to the problems of flood routing, tidal circulation, storm surges, and atmospheric circulation. These methods are often based on the Alternating Direction Implicity(ADI) method. However, the ADI method results in inaccuracies for large time steps when dealing with a complex geometry or bathymetry. Since this method reduces the performance considerably, a fully implicit method developed by Wilders et al. (1998) is used to improve the accuracy for a large time step. Finite Difference Methods are defined on a rectangular grid. Two drawbacks of this type of grid are that grid refinement is not possibile locally and that the physical boundary is sometimes poorly represented by the numerical model boundary. Because of the second deficiency several purely numerical boundary effects can be involved. A boundary fitted curvilinear coordinate transformation is used to reduce these difficulties. It the curvilinear coordinate transformation is used to reduce these difficulties. If the coordinate transformation is orthogonal then the transformed shallow water equations are similar to the original equations. Therefore, an orthogonal coorinate transformation is used for defining coordinate system. A multigrid (MG) method is widely used to accelerate the convergence in the numerical methods. In this study, a technique using a MG method is proposed to reduce the computing time and to improve the accuracy for the orthogonal to reduce the computing time and to improve the accuracy for the orthogonal grid generation and the solutions of the shallow water equations.