• Tribology and Lubricants
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• v.16 no.4
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• pp.295-301
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• 2000

The dynamic simulation of slider in hard disk drive is performed using Factored Implicit Finite Difference method. The modified Reynolds equation with Fukui and Kaneko model is employed as a governing equation. Equations of motion for the slider of three degrees of freedom are solved simultaneously with the modified Reynolds equation. The transient responses of the slider for disk step bumps and slider impulse forces are shown for various cases and are compared for the iteration algorithm and new algorithm.

• Journal of Information Processing Systems
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• v.14 no.5
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• pp.1068-1074
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• 2018

In this paper, we consider the delay partial differential equation of three dimensions with constant coefficients. We established the alternating direction difference scheme by the standard finite difference method, gave the order of convergence of the format and the expression of the difference scheme truncation errors.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.225-228
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• 1999

In a plastically deformed body the formation of a shear band is widely observed in the engineering materials during rapidly forming process for a thermally rate-sensitive material. The localized shear bond stems from evolution of a narrow region in which intensive plastic flow occurs. The shear band often plays as a precursor of the ductile fracture during a forming process. The objectives of this study are to investigate the localization behaivor by using numerical method thus predict the failure. In this work the implicit finite difference scheme is preformed due to the ease of covergence and the numerical stability. This study is based on an analysised material with hardening as well as thermally softening behavior which includes isotropy strain hardening. Furthermore this paper suggests that an anticipated and suggested a kinematic hardening constitutive equation be requried to predicte a more accurate strain level wherein a shear band occurs.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.7-12
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• 1998

Optimized high-order compact(OHOC) schemes were proposed, which have high spatial order of truncation and resolution to simulate the aeroacoustic problems due to unsteady compressible flows. Generally, numerical schemes are categorized explicit or implicit by time-marching method. In this research, OHOC differences which were developed with explicit time-marching method is used to have implicit formulation and the implicit OHOC differences result in block hepta-diagonal matrix. This paper presents the comparisons between the explicit and implicit OHOC schemes with a second order accuracy of time in the 1-d linear wave convection problem, and between the explicit OHOC scheme of 4th-order accuracy in time and the implicit OHOC scheme of 1st-order accuracy in tine for the 1-d nonlinear wave convection problem. With these comparisons, the characteristics of implicit OHOC scheme are shown in the point of CFL number.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.1-13
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• 2002

In this paper we present numerical methods fur computations of nonequilibrium hypersonic flow of air around bodies including chemical reaction effects and present numerical result of the flow over concave corners. We developed implicit finite difference method to overcome numerical difficulties with the lack of resolution behind the shock and near the body. Using our method we were able to find details of the flow properties near the shock and body and were able to continue the computation of the flow for a long distance from the corner of the body.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• Journal of computational fluids engineering
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• v.2 no.1
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• pp.8-12
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• 1997

The three-dimensional Euler equations are solved numerically for the analysis of contraction flows in wind or water tunnels. A second-order finite difference method is used for the spatial discretization on the nonstaggered grid system and the 4-stage Runge-Kutta scheme for the numerical integration in time. In order to speed up the convergence, the local time stepping and the implicit residual-averaging schemes are introduced. The pressure field is obtained by solving the pressure-Poisson equation with the Neumann boundary condition. For the evaluation of the present Euler solver, numerical computations are carried out for three contraction geometries, one of which was adopted in the Large Cavitation Channel for the U.S. Navy. The comparison of the computational results with the available experimental data shows good agreement.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.881-898
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• 2018

This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.329-341
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• 2021

In this study, we consider an efficient and accurate finite difference method for the four underlying asset equity-linked securities (ELS). The numerical method is based on the operator splitting method with non-uniform grids for the underlying assets. Even though the numerical scheme is implicit, we solve the system of discrete equations in explicit manner using the Thomas algorithm for the tri-diagonal matrix resulting from the system of discrete equations. Therefore, we can use a relatively large time step and the computation of the ELS option pricing is fast. We perform characteristic computational test. The numerical test confirm the usefulness of the proposed method for pricing the four underlying asset equity-linked securities.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.39 no.10
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• pp.38-45
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• 2002

This paper presents the new Compact 2D ADI-FDTD(Alternating-Direction Implicit Finite-Difference Time-Domain) method, where the time step is no longer restricted by the numerical stability condition. This method is an accelerating algorithm for the conventional Compact 2D FDTD method. To validate this algorithm, we have analyzed the dispersion characteristics of the hollow rectangular waveguide and the shielded microstrip line. The results of the proposed method are very well agreed with those of both the conventional analytic method and the Compact 2D FDTD method. The CPU time for analysis of this method is very much reduced compared with the conventional Compact 2D FDTD method. The proposed method is valuable as a fast algorithm in the research of dispersion characteristics of the waveguide structures.