• 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.

• 유체기계공업학회:학술대회논문집
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• 1999.12a
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• pp.163-169
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• 1999

The numerical procedure has been developed for simulating incompressible viscous flow around a turbine stage with rotor-stator interaction. This study solves 2-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system. The Marker-and-Cell concept is applied to efficiently solve continuity equation. To impose an accurate boundary condition, O-H multiblocked grid system is generated. O-type grid and H-type grid is generated near and outer rotor-stator The cubic-spline interpolation is applied to handle a relative motion of a rotor to the stator. Turbulent flows have been modeled by the Baldwin- Lomax turbulent model. To validate present procedure, the time averaged pressure coefficients around the rotor and stator are compared with experiment and a good agreement obtained.

• Journal of Advanced Marine Engineering and Technology
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• v.30 no.3
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• pp.369-375
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• 2006

Large eddy simulation has been applied to simulate turbulent flow around a cubic obstacle mounted on a channel surface for a Reynolds number of 40000(based on the incoming bulk velocity and the obstacle height) using a Smagorinsky model and a Lagrangian dynamic model. In order to develop the LES to the practical engineering application, the effect of upwind scheme, turbulent sub-grid scale model were investigated. The computed velocities. turbulence quantifies, separation and reattachment length were evaluated by compared with the previous experimental results.

• Journal of computational fluids engineering
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• v.13 no.3
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• pp.28-34
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• 2008

In engineering application of large eddy simulation, there are still questions as follows grid dependency on numerical results, the effect of upwind scheme against a calculation instability, appropriate boundary conditions dealing with turbulence fluctuation and the performance of SGS models. In this study, in order to develop the LES to the engineering application, large eddy simulation was carried out to investigate the effect of upwind scheme, turbulent subgrid model and the grid dependancy of the flow around a wall-mounted cube in a channel at Re=40,000 based on cubic height and bulk mean velocity. The computed velocities, turbulence quantities, separation and reattachment length were evaluated compared with the experimental results of R. Matinuzzi and C. Tropea.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.45 no.3
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• pp.226-232
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• 2017

Surface pressure distributions over the RAE-A wing-body configuration were investigated and the grid convergence along the streamwise, spanwise, and circumferential directions was numerically studied. Flow analysis in subsonic and transonic conditions was conducted using the $k-{\omega}$ Wilcox-Durbin+ turbulence model. Surface pressure distributions for subsonic flows were well matched, but those for transonic shocked flows showed a little discrepancy with the experimental data. A cubic spline extrapolation method was applied in order to investigate the grid convergence. This method presented that the grid resolution in the circumferential direction is the most important grid parameter. A refined grid system was made based on the grid convergence study and provided more accurate prediction, especially on the symmetric body surface of RAE-A configuration.

• Journal of Environmental Impact Assessment
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• v.19 no.5
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• pp.465-473
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• 2010

This study was carried out to investigate the effect of EFDC hydrodynamic result on the WASP7.3 water quality modeling result in accordance with the change of number of grid for the dam reservoir to be constructed. The simulated flow and BOD, T-N and T-P loads by the HSPF watershed model was used for boundary conditions and the hydrodynamic modeling results was linked with WASP model to predict future water quality after dam construction. The scenarios for EFDC modeling were composed of Scenario 1(141 grid cells) and Scenario 2(568 grid cells). The results of Scenario 2 showed that BOD, T-N, T-P and Chl-a concentrations were decreased 0.073mg/L(8.5%), 0.032mg/L(2.6%), 0.003mg/L(6.8%), 0.644mg/L(4.2%) compared with those of Scenario 1, respectively. As number of grid cell increased, water quality concentrations were decreased and also it caused the longer running time. Therefore, this study suggests that the consideration of the geometry of water body is more important than the number of grid cells for the prediction of water quality of a dam reservoir in EIA.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.6
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• pp.26-34
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• 2008

The information of traversability and path planning is essential for UGV(Unmanned Ground Vehicle) navigation. Such information can be obtained by analyzing 3D terrain. In this paper, we present the method of 3D terrain modeling with color information from a camera, precise distance information from a 2D Laser Range Finder(LRF) and wheel encoder information from mobile robot with less data. And also we present the method of 3B terrain modeling with the information from GPS/IMU and 2D LRF with less data. To fuse the color information from camera and distance information from 2D LRF, we obtain extrinsic parameters between a camera and LRF using planar pattern. We set up such a fused system on a mobile robot and make an experiment on indoor environment. And we make an experiment on outdoor environment to reconstruction 3D terrain with 2D LRF and GPS/IMU(Inertial Measurement Unit). The obtained 3D terrain model is based on points and requires large amount of data. To reduce the amount of data, we use cubic grid-based model instead of point-based model.

• Fire Science and Engineering
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• v.11 no.4
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• pp.3-14
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• 1997

The smoke filling process for the atrium space containing a fire source is simulated using two types of deterministic fire model : Zone model and Field model. The zone model used is the CFAST(version 1.6) model developed at the Building and Fire Research Laboratories, NIST in the USA. The field model is a self-developed frie field model based on Computational Fluid Dynamic (CFD) theories. This article is focused on finding out the smoke movement and temperature distribution in atrium space which is cubic in shape. For solving the liked set of velocity and pressure equation, the PISO algorithm, which strengthened the velocity-pressure coupling, was used. Since PISO algorithm is a time-marching procedure, computing time si very fast. A computational procedure for predicting velocity and temperature distribution in fire-induced flow is based on the solution, in finite volume method and non-staggered grid system, of 3-dimensional equations for the conservation of mass, momentum, energy, species and so forth. The fire model i.e Zone model and Field model predicted similar results for clear heights and the smoke layer temperature.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.8
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• pp.1063-1071
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• 1999

Fine grid calculations are reported for the developing turbulent flow in a curved duct of square cross-section with a radius of curvature to hydraulic diameter ratio ${\delta}=Rc/D_H=3.357 $ and a bend angle of 720 deg. A sequence of modeling refinements is introduced; the replacement of wall function by a fine mesh across the sublayer and a low Reynolds number algebraic second moment closure up to the near wall sublayer in which the non-linear return to isotropy model and the cubic-quasi-isotropy model for the pressure strain are adopted; and the introduction of a multiple source model for the exact dissipation rate equation. Each refinement is shown to lead to an appreciable improvement in the agreement between measurement and computation.

• Journal of Environmental Science International
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• v.11 no.9
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• pp.907-914
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• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.