• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.75-81
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• 2003

Compact schemes are shown to be effective for a class of problems including convection-diffusion equations when combined with multigrid algorithms [7, 8] and V-cycle convergence is proved[5]. We apply the multigrid algorithm for an semianalytic finite difference scheme, which is desinged to preserve high order accuracy despite of singularities.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.135-142
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• 2000

We consider a multigrid algorithm for higher order finite difference scheme for the Poisson problem on rectangular domain. Several smoothers including Jacobi, Red-black Gauss-Seidel are tested and compared. Since higher order scheme gives much more accurate result then 5-point scheme, one may use small number of levels with higher order scheme and thus the overall cost is reduced quite a lot. The numerical experiment compares the two cases.

• Journal of computational fluids engineering
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• v.11 no.1 s.32
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• pp.36-42
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• 2006

The existing numerical approximations of convection flux, especially the spatial higher-order difference schemes, in unstructured cell-centered finite volume methods are examined in detail with each other and evaluated with respect to the accuracy through their application to a 2-D benchmark problem. Six higher-order schemes are examined, which include two second-order upwind schemes, two central difference schemes and two hybrid schemes. It is found that the 2nd-order upwind scheme by Mathur and Murthy(1997) and the central difference scheme by Demirdzic and Muzaferija(1995) have more accurate prediction performance than the other higher-order schemes used in unstructured cell-centered finite volume methods.

• Journal of the korean Society of Automotive Engineers
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• v.3 no.3
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• pp.24-29
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• 1981

This paper is studied an efficient temperature distribution and heat transfer of two-dimensional rectangular cross-section by the higher-order triangular finite dynamic element and finite difference. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and convection matrices. Numerical solution results of temperature distribution presented herein clearly optimum element and show that FEM10 is the most accurate temperature distribution, but heat transfer and computational effort is the most acquired.

• Journal of computational fluids engineering
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• v.7 no.1
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• pp.28-35
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• 2002

The effect of concave curvature on the natural convection has been numerically studied using the higher-order finite difference method. The heating wall in a enclosure is approximated by a cosine function. The heat transfer coefficient is analyzed for three Rayleigh numbers and five amplitudes. For Ra = 10/sup 8/ the separation and reattachment are observed on the adiabatic walls. The wall heat transfer are slightly changed by the increasing curvatures.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.1
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• pp.38-44
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• 2010

In this paper, the higher order FDTD(Finite-Difference Time-Domain) method is used to obtain the frequency response characteristics of the cylindrical metamaterial slab. FDTD method is one of strongest electromagnetic numerical method which is widely used to analyze the metamaterial structure because of its simplicity and the dispersive FDTD equation which has the dispersive effective dielectric constant and permeability are derived to analyze the metamaterials. This derived dispersive FDTD equation has no errors in analyzing the dielectric materials but there are some time and frequency errors in case of analyzing the metamaterials. We used the higher order FDTD method to obtain the accurate frequency response of the metamaterials. Comparisons between the dispersive FDTD method and the higher order FDTD method are performed in this paper also. From the results, we concluded that more accurate frequency response for various metamaterials applications can be obtained using the proposed method in this paper.

• Journal of Ocean Engineering and Technology
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• v.12 no.2 s.28
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• pp.97-110
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• 1998

The numerical damping and dispersion error characteristics associated with difference schemes and a panel shift method used for the calculation of steady free surface flows by a panel method are an analysed in this paper. First, 12 finite difference operators used for the double model flow by Letcher are applied to a two dimensional cylinder with the Kelvin free surface condition and the numerical errors with these schemes are compared with those by the panel shift method. Then, 3-D waves due to a submerged source are calculated by the difference schemes, the panel shift method and also by a higher order boundary element method(HOBEM). Finally, the waves and wave resistance for Wigley's hull are calculated with these three schemes. It is shown that the panel shift method is free of numerical damping and dispersion error and performs better than the difference schemes. However, it can be concluded that the HOBEM also free of the numerical damping and dispersion error is the most stable, accurate and efficient.

• Journal of Hydrospace Technology
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• v.2 no.2
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• pp.57-67
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• 1996

The formulation for hybrid-QUICK scheme of convective transport terms in finite-volume calculation procedure is presented. Source terms are modified to apply the hybrid-QUICK scheme. Test calculations are performed for wall-driven cavity flow at Re=$10_2$, $10_3$, and $10_4$. These include the evaluation of boundary conditions approximated by third-order finite difference scheme. The stable and converged solutions are obtained without unsteady terms in the momentum equations. The results using hybrid-QUICK scheme show no difference with those using hybrid scheme at low Re ($=10_2$) and are better at higher Re ($10_3$, and $10_4$).

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1365-1381
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• 1990

A $C^{0}$ continuous displacement finite element method based on a higher-order shear deformation theory is employed in the prediction of the transient response of laminated composite plates subjected to low-velocity impact. A modified contact law was applied to calculate the contact force during impact. The discrete element chosen is a nine-noded quadrilateral with 5 degree-of-freedom per node. The Wilson-.theta. time integration algorithm is used for solving the time dependent equations of the impactor and the central difference method was adopted to perform time integration of the plate. Numerical results, including the contact force history, deflection, and velocity history, are presented. Comparisons of numerical results using a higher order theory and a first-order theory show that using a higher order theory provides more accurate results. Effects of boundary condition, impact velocity, and mass of the impactors are also discussed.d.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.10 no.6
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• pp.847-854
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• 1999

In this paper, we have analysed frequency-dispersion characteristics of higher-order modes for uniform planar transmission lines, using the 2-dimensional finite-difference time-domain method. The method presented in this paper uses both informations of amplitude and phase of the electromagnetic spectrum to determine resonant frequencies, while methods previously reported use the magnitude only. This algorithm is very useful when a resonant mode has a relatively small magnitude, where the identification of the resonant mode is quite difficult. Numerical results show that a strip line supports few higher-order modes within the frequency range of 20 GHz, but there occur many higher-order modes in the structure of grounded coplanar waveguide, where resonant frequencies of the first higher-order mode is very close to those of the fundamental mode and there occur lots of very adjacent higher-order modes. As in this example, for the analysis of planar transmission lines which support many resonant modes very close each other, the method presented in this paper can be applied very efficiently.