• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.336-347
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• 1992

The three dimensional inviscid transonic cascade flow was investigated numerically, incorporation a four stage Runge-Kutta integration method proposed by Jameson. Time marching to the steady state was accelerated by using optimum time step and enthalpy damping. In describing the boundary conditions at inlet and outlet, Riemann invariants are considered. By adding a second and a fourth order artificial viscocities, the numerical instability due to the propagation of undamped disturbance or the rapid change of state near the shock has been prevented. The numerical results for are bump cascade, cambered two dimensional turbine cascade and three dimensional stator cascade agreed reasonably well with previous results. It has been known that the accuracy of the solution depended a lot on the modeling of the leading or trailing edge.

• Journal of computational fluids engineering
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• v.8 no.3
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• pp.50-55
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• 2003

Recent numerical simulation has a tendency to require the higher-order accuracy in time, as well as in space. This tendency is more true in LES and acoustic noise simulation. In the present work, the accuracy of a Fractional step method, which is widely used in LES simulation, has been increased to the fourth-order accurate compact Pade discretization. To validate the present code, the flow-field past a cylinder was simulated and compared with experiment. A good agreement with experiment was achieved.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.3
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• pp.149-155
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• 1999

A treatment of wave breaking is included in the extended Boussinesq equations of Nwogu. A spatially distributed source function and sponge layers are used to reduce the reflected waves in the computa¬tional domain. The model uses fourth-order Adams predictor-corrector method to advance in time, and discretizes first-order spatial derivatives to fourth-order accuracy, and thus reducing all truncation errors to a level smaller than the dispersive terms. The generated wave fields are found to be good and the corresponding wave heights are very close to their target values. For the tests of wave breaking, although agreement is considered to be reasonable, wave heights in the inner surf zone are over-predicted. This indicates the breaking parameters in the model should be adjusted.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.2
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• pp.129-136
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• 2011

The aim of this paper is to present the method of identifying the impact location on the plate. This basic research has the future purpose to achieve the human-interaction technology based on the signal processing, piezoelectric materials, and wave propagation. The present work concerning the location identification of a single impact on the plate simulated the waveform numerically generated by impact force and applied the SWFOM(sliced Wigner higher fourth order moment) to the waveform to get the arrival time differences due to impact force between three sensors attached to the plate. The simulated signal is useful to get the information for time interval for the only direct wave. This information is used the source localization by using experimental work. The measured signal is also used for source localization of a single impact based on the higher order time frequency as a novel work.

• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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• pp.1-16
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• 2017

The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of the original equation using the solutions of the subproblems. The purpose of this paper is to characterize higher order operator splitting schemes and propose several higher order methods. Unlike the first and the second order methods, each of the heat and the free-energy evolution operators has at least one backward evaluation in higher order methods. We investigate the effect of negative time steps on a general form of third order schemes and suggest three third order methods for better stability and accuracy. Two fourth order methods are also presented. The traveling wave solution and a spinodal decomposition problem are used to demonstrate numerical properties and the order of convergence of the proposed methods.

• International Journal of Aeronautical and Space Sciences
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• v.9 no.2
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• pp.79-86
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• 2008

High performance direct-iterative hybrid linear solver for large scale finite element problem is developed. Direct solution method is robust but difficult to parallelize, whereas iterative solution method is opposite for direct method. Therefore, combining two solution methods is desired to get both high performance parallel efficiency and numerical robustness for large scale structural analysis problems. Hybrid method mentioned in this paper is based on FETI-DP (Finite Element Tearing and Interconnecting-Dual Primal method) which has good parallel scalability and efficiency. It is suitable for fourth and second order finite element elliptic problems including structural analysis problems. We are using the hybrid concept of theses two solution method categories, combining the multifrontal solver into FETI-DP based iterative solver. Hybrid solver is implemented for our general structural analysis code, IPSAP.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.8
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• pp.969-977
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• 1999

A similarity solution of a steady laminar flow of micropolar fluids past wedges has been studied. The similarity variables found by Falkner and Skan are employed to reduce the streamwise-dependence in the coupled nonlinear boundary layer equations. Numerical solutions of the equations are then obtained using the fourth-order Runge-Kutta method and the distribution of velocity, micro-rotation, shear and couple stress across the boundary layer are obtained. These results are compared with the corresponding flow problems for Newtonian fluid past wedges with various wedge angles. Numerical results show that, keeping ${\beta}$ constant, the skin friction coefficient is lower for a micropolar fluid, as compared to a Newtonian fluid. For the case of constant material parameter K, however, the velocity distribution for a micropolar fluid is higher than that of a Newtonian fluid.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.3
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• pp.245-256
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• 2014

This work is focused on the boundary layer and heat transfer characteristics of hydromagnetic flow over a stretching sheet with variable thickness. Steady, two dimensional, nonlinear, laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness and power law velocity in the presence of variable magnetic field and variable temperature is considered. Governing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The resulting non-linear differential equations are solved numerically by utilizing Nachtsheim-Swigert shooting iterative scheme for satisfaction of asymptotic boundary conditions along with fourth order Runge-Kutta integration method. Numerical computations are carried out for various values of the physical parameters and the effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained.

• Bulletin of the Korean Chemical Society
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• v.15 no.6
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• pp.488-496
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• 1994

An approximate nonlinear theory of the Oregonator model is obtained with the aid of an ordinary perturbation method when the system is perturbed by some kinds of external input. The effects of internal and external parameters on the oscillations are discussed in detail by taking specific values of the parameters. A simple approximate solution for the Oregonator model under the influence of a constant input is obtained and the result is compared with the numerical result. For other types of external inputs the approximate solutions up to the fourth order expansion are compared with the numerical results. For a periodic input, we found that the entrainment depends crucially on the difference between the internal and external frequencies near the bifurcation point.