• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.2
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• pp.479-491
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• 1994

Discrete vortex method was applied for simulating an active control of turbulent leading- edge separation bubble. The leading-edge separation zone was perturbed by a time-dependent sinusoidal perturbation of different frequencies and levels. In order to describe the local sinusoidal perturbation at the separation point, a source pulsation vortex technique was proposed. The present two-dimensional vortex simulations were qualitatively compared with the experimental results for a blunt circular cylinder, where perturbation was introduced along the square-cut leading edge of the cylinder $(Kiya et al.^{(6,7)}).$ It was found that the reattachment length attained a minimum point at low levels of perturbation and two minima at a moderate higher perturbation frequency. The effects of local perturbation on the evolution of leading-edge separation bubble were scrutinized by comparing the perturbed flow with the natural flow. These comparisons were made for the distributions of mean velocity and its velocity fluctuations, intermittency and wall velocity. The motions of instantaneous reattachment in the space-time domain were demonstrated, which were also compared with the experimental findings. In order to investigate the reduction mehanism of reattachment length in the separation bubble, various cross-correlations for velocity and pressure and the relevant convection velocities were evaluated. It was observed that the convection velocity was closely associated with its corresponding pulsationg frequency.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1279-1292
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• 2009

In this paper, a numerical method that uses standard finite difference scheme defined on Shishkin mesh for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.77.1-77.1
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• 2016

We investigate the properties and detection conditions for the planetary caustic perturbation of close-separation planets. To find the properties of the planetary caustic perturbation, we construct deviation maps by subtracting the single-lensing magnification of the lens star from the planetary lensing magnification for various lensing parameters. We find that each deviation area of the positive and negative perturbations disappears at the same normalized source radius according to a given deviation threshold regardless of mass ratio but disappears at a different normalized source radius according to the separation. We also estimate the upper limit of the normalized source radius to detect the planetary caustic perturbation. We find simple relations between the upper limit of the normalized source radius and the lensing parameters. From the relations, we obtain an analytic condition for the detection limit of the planet, and which show that we can sufficiently discover a planet with the mass of sub-Earth for typical microlensing events. Therefore, we expect to add the number of low-mass planets in the next-generation microlensing experiments and conclude that our detection condition of the planet can be used as a important criteria for maximal planet detections considering the source type and the photometric accuracy.

• The Bulletin of The Korean Astronomical Society
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• v.35 no.1
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• pp.48.1-48.1
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• 2010

Four of nine exoplanets found by microlensing were detected by the resonant caustic, which represents the merging of the planetary and central caustics at the position when the projected separation of a host star and a bounded planet is s~1. One of the resonant caustic lensing events, OGLE-2005-BLG-169, was a caustic-crossing high-magnification event with A_max ~800 and the source star was much smaller than the caustic, nevertheless the perturbation was not obviously apparent on the light curve of the event. In this paper, we investigate the perturbation pattern of the resonant caustic to understand why the perturbations induced by the caustic do not leave strong traces on the light curves of high-magnification events despite a small source/caustic size ratio. From this study, we find that the regions with small magnification excess around the center of the resonant caustic are rather widely formed, and the event passing the small-excess region produces a high-magnification event with a weak perturbation that is small relative to the amplification caused by the star and thus does not noticeably appear on the light curve of the event. We also find that the positive excess of the inside edge of the resonant caustic and the negative excess inside the caustic become stronger and wider as q increases, and thus the resonant caustic-crossing high-magnification events with the weak perturbation occur in the range of q $\leq$ 10-4. We determine the probability of the occurrence of events with the small excess $|\varepsilon|{\leq}3%$ in high-magnification events induced by a resonant caustic. As a result, we find that for the Earth-mass planets with a separation of ~2.5 AU the resonant caustic high-magnification events with the weak perturbation can occur with a significant frequen.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.635-648
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• 2015

We consider a weakly coupled system of singularly perturbed convection-diffusion equations with discontinuous source term. The diffusion term of each equation is associated with a small positive parameter of different magnitude. Presence of discontinuity and different parameters creates boundary and weak interior layers that overlap and interact. A numerical method is constructed for this problem which involves an appropriate piecewise uniform Shishkin mesh. The numerical approximations are proved to converge to the continuous solutions uniformly with respect to the singular perturbation parameters. Numerical results are presented which illustrates the theoretical results.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2003.10a
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• pp.65-70
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• 2003

In this work variations of orbital parameters are first derived from the perturbation equations using difference equation method under Earth oblateness and atmospheric drag. A simple and effective scheme is proposed to compute the required delta v and fuel consumption to compensate for atmospheric drag. The scheme is applied to KOMPSAT example. And by means of numerical simulations we quantitatively analyze influences due to each perturbation source, i.e., nonspherical Earth, atmospheric drag, third body gravities (Sun, Moon), and solar radiation.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.16 no.2
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• pp.77-84
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• 1980

The nonstationary vibration of a rotor carrying two discs with a limited driving torque is studied theoretically by using the method of the perturbation theory. The influence of the asymmetry, torque, damping and phase difference in passing through a critical speed is studied in detail, considering the interaction between the driving source and the vibration system.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.4
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• pp.245-275
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• 2017

The present investigation deals, Dufour and heat source effects on radiative MHD slip flow of a viscous fluid in a parallel porous plate channel in presence of chemical reaction. The non-linear coupled partial differential equations are solved by using two term perturbation technique subject to physically appropriate boundary conditions. The numerical values of the fluid velocity, temperature and concentration are displayed graphically whereas those of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. By increasing the slip parameter at the cold wall the velocity increases whereas the effect is totally reversed in the case of shear stress at the cold wall. It is observed that the effect of Dufour and heat source parameters decreases the velocity and temperature profiles.

• The Journal of the Acoustical Society of Korea
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• v.15 no.2E
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• pp.45-49
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• 1996

From the reverberation signals received in the shallower water, the surface scattered signals are identified by using the multipath eigneray model that provides launch angles, grazing angles and transmission loss from the high frequency directional source to and from the rough surface. For small scale surface waves, the perturbation method is used to compute the backscattering strength for various grazing angles and wind speeds. A scheme to inversely estimate the wind speed, by which the observed surface reverberation levels are produced, has been tested. In result, for low grazing angles the perturbation method can be used to predict the backscattering stregth, thereby the surface wind can be indirectly estimated.