• Journal of Korean Society of Coastal and Ocean Engineers
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• v.3 no.2
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• pp.81-91
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• 1991

A k-$\varepsilon$ equation model was established to investigate the behaviours of two-dimensional surface buoyant jets. Its computational results were compared with experimental data on the mean flow and the turbulent transport. The model was proved to predict the flow characteristics reasonably. The influence of the values of k and $\varepsilon$ given in the inlet on the evaluation of surface buoyant jets was examined to determine them quantitatively. Computations for several values of buoyancy production coefficient $C\varepsilon$$_3$ in the $\varepsilon$ equation, which has been neglected by many researchers. were carried out to evaluate its effect on the flow development. Computational results of the two-dimensional surface buoyant jets were presented and briefly discussed.

• Industrial Engineering and Management Systems
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• v.9 no.4
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• pp.323-338
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• 2010

In this paper, we introduce the implied volatility from Black-Scholes model and suggest a model for constructing implied volatility surfaces by using the two-dimensional cubic (bi-cubic) spline. In order to utilize a spline method, we acquire grid (knot) points. To this end, we first extract implied volatility curves weighted by trading contracts from market option data and calculate grid points from the extracted curves. At this time, we consider several conditions to avoid arbitrage opportunity. Then, we establish an implied volatility surface, making use of the two-dimensional cubic spline method with previously estimated grid points. The method is shown to satisfy several properties of the implied volatility surface (smile, skew, and flattening) as well as avoid the arbitrage opportunity caused by simple match with market data. To show the merits of our proposed method, we conduct simulations on market data of S&P500 index European options with reasonable and acceptable results.

• Geomechanics and Engineering
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• v.25 no.3
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• pp.221-231
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• 2021

A two dimensional model of linearly elastic soil spring used for the settlement analysis of the flexible mat foundation is suggested in this study. The spring constants of the soils underneath the foundation were modeled assuming uniformly vertical load applied onto the foundation. The soil spring constants were back calculated using the three-dimensional finite element analysis with Midas GTS NX program. Variation of the soil spring constants was modeled as a two-dimensional polynomial function in terms of the normalized spatial distances between the center of foundation and the analytical points. The Lysmer's analog spring for soils underneath the rigid foundation was adopted and calibrated for the flexible foundation. For validations, the newly proposed soil spring model was incorporated into a two dimensional finite difference analysis for a square mat foundation at the surface of an elastic half-space consisting of soft clays. Comparative study was made for elastic soils where the shear wave velocity is 120~180 m/s and the Poisson's ratio varies at 0.3~0.5. The resulting foundation settlements from the two dimensional finite difference analysis with the proposed soil springs were found in good agreement with those obtained directly from three dimensional finite element analyses. Details of the applications and limitations of the modified Lysmer's analog springs were discussed in this study.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.10
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• pp.1436-1444
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• 2002

A three dimensional numerical model was developed to analyze the mold filling and solidification processes straightforwardly in a casting processes. On the basis of the SIMPLER algorithm, the VOF method and the Equivalent Specific Heat method were adopted to deal with the free surface behavior and the latent heat evolution. The complete model has been validated using exact solutions and experimental results. The importance of three-dimensional effects has been highlighted by comparing the results from the three-dimensional analysis with those given by a two-dimensional analysis.

• Journal of the Society of Naval Architects of Korea
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• v.51 no.5
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• pp.435-449
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• 2014

The effects of the gravity field and the free surface on the cavity shape and the drag are investigated through a numerical analysis for the steady supercavitating flow past a simple two-dimensional body underneath the free surface. The continuity and the RANS equations are numerically solved for an incompressible fluid using a $k-{\epsilon}$ turbulence model and a mixture fluid model has been applied for calculating the multiphase flow of air, water and vapor using the method of volume of fluid and the Schnerr-Sauer cavitation model. Numerical solutions have been obtained for the supercavitating flow about a two-dimensional $30^{\circ}$ wedge in wide range of depths of submergence and inflow velocities. The results are presented for the cavity shape, especially the length and the width, and the drag of the wedge in comparison with those of the case for the infinite fluid flow neglecting the gravity and the free surface. The influences of the gravity field and the free surface on the aforementioned quantities are discussed. The length and the width of the supercavity are reduced and the centerline of the cavity rises toward the free surface due to the effects of the gravity field and the free surface. The drag coefficient of the wedge, however, is about the same except for shallow depths of submergence. As the supercavitating wedge is approaching very close to the free surface, it is found the length and the width of a cavity are shorten even though the cavitation number is reduced. Also the present result suggests that, under the influence of the gravity field and the free surface, the length of the supercavity for a certain cavitation number varies and moreover is proportional to the inverse of the submergence depth Froude number.

• Journal of Industrial Technology
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• v.26 no.A
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• pp.129-137
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• 2006

In this research, we made a one and two-dimensional analysis of numerical data collected from the bend curvature of a bended river section. According to the result from the numerical analysis, the inflow ＆ output angle caused a water level deviation which increased with an increase of the flood discharge. From the water level deviation of our two-dimensional numerical model, we obtained the maximum slope of 6,67% when the inflow and output angle was 105 degrees and the flood discharge was 500 CMS. As for the right side, the differences with the one-dimensional numerical model were reduced when the angle was more than $90^{\circ}$. As for the left side the differences were reduced when the angle was more than $105^{\circ}$. For a river with more than 90 degrees bend curvature, a hydraulic experiment would be more appropriate than a numerical analysis.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.11
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• pp.1862-1870
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• 1997

A fast and precise technique to measure 3-dimensional coordinates of an object is proposed. It is essential to take the 3-dimensional measurements of the object in design and inspection. Using this developed system a surface model of a complex shape can be constructed. 3-dimensional world coordinates are projected onto a camera plane by the perspective transformation, which plays an important role in this measurement system. According to the shape of the object two measuring methods are proposed. One is rotation of an object and the other is translation of measuring unit. Measuring speed depending on image processing time is obtained as 200 points per second. Measurement resolution i sexperimented by two parameters among others; the angle between the laser beam plane and the camera, and the distance between the camera and the object. As a result of these experiments, it was found that measurement resolution ranges from 0.3mm to 1.0mm. This constructed surface model could be used in manufacturing tools such as rapid prototyping machine.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.3
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• pp.248-256
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• 1995

The numerical study on the surface buoyant jets has remained of requiring more intensive investigation for problems due to the treatments of free surface, Reynolds stress/flux terms in turbulent flow and especially buoyancy effects on the turbulent fluctuation. etc. The verification of predicted results from the numerical study continues in the qualitative study. because of the lack of experimental data, which seems to be due to the difficulties in measuring the turbulent fluctuations in concentration or temperature fields. In this study, the computer program of Algebraic Stress Model has been developed to investigate the behaviours of two-dimensional surface buoyant jets with free surface boundary condition. The computational results are compared with published experimental data. By comparing these results with experimental data. it is found that this model can predict fairly well the flow characteristics of two-dimensional surface buoyant jets in the momentum-dominant region and buovancy-dominant region. Especially, it is proved that this model can predict the flow characteristics reasonably in buoyancy-dominant region stably stratified due to buoyancy effect.

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.3
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• pp.3-14
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• 2004

A two-dimensional numerical model based on a finite volume method was formulated to solve the shallow water equations and applied for evaluating drainage characteristics at large-sized paddy fields. Manning roughness coefficient was calibrated using the observed inundating depths at drainage tests, and used for validating the model with the results from another drainage test. The simulated results were in good agreement with the observed inundating depths. The result of surface drainage showed that the longer width of the outlet was or the more the number of drainage outlet was, the shorter the drainage time was taken, and the larger the size of the field become, the longer the drainage time was taken, and the field shape had little effect on drainage time. To reduce the drainage time to 24 hours, the outlet is located lower than the elevation of the basin and small drainage ditch is constructed at the field. The results showed that the drainage time was taken short as the small drainage ditch was constructed. The comparison of drainage time as to the size of field constructed small drainage ditch showed the field, 100m ${\times}$ 200 m, can be drained in 24 hours.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.7
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• pp.99-104
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• 2003

A precision displacement measurement system of 3-DOF micro motions is proposed in this paper. The measurement system is composed of two diode lasers, two quadratic PSDs, two beam splitters and a sphere whose surface is highly reflective. In this measurement system, the sphere reflector is mounted on the platform of positioning devices whose 3-DOF translational motions are to be measured, and the sensitive areas of two PSDs are oriented toward the center point of the sphere reflector. Each laser beam emitted from two diode laser sources is reflected at the surface of sphere and arrives at two PSDs. Each PSD serves as a 2-dimensional sensor, providing the information on the 3-dimensional position of the sphere. In this paper, we model the relationship between the outputs of two PSDs and 3-DOF translational motions of the sphere mounted on the object. Based on a deduced measurement model, we perform measurement simulation and evaluate the performance of the proposed measurement system: linearity, sensitivity, and measurement error. The simulation results show that the proposed measurement system can be valid means of precision displacement measurement of 3-dimensional micro motions.