• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1087-1100
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• 2014

We present an accurate and efficient numerical method for solving the Black-Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid generation: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demonstrate the accuracy and efficiency of the proposed method. The results show that the computational time is reduced substantially with the accuracy being maintained.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2003.10a
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• pp.99-103
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• 2003

An analysis of the flow within supersonic turbine cascades is necessary to design and manufacture turbo-pump system. Because of the differences between the specified inlet boundary value and the computed inlet value caused by the far field inlet boundary condition, the computations at desired inlet conditions can not be achieved. So, this paper studied the problem occurred when far field inlet conditions were specified as inlet boundary conditions. And the numerical analyses using Fine Turbo, CFD Program, has been performed and compared with those of experiments when a converging-diverging nozzle or a linear nozzle was located in front of cascades instead of the far field inlet condition.

• International Journal of Aeronautical and Space Sciences
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• v.6 no.1
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• pp.1-7
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• 2005

The inlet boundary condition of computations about the supersonic turbine flow is commonly applied as far-field inlet boundary condition with specified velocity. However, the inflow condition of supersonic turbine is sometimes affected by the shocks or expansion waves propagated from leading edges of blade. These shocks and expansion waves alter the inlet boundary condition. In this case, the inlet boundary condition can not be specified Therefore, in this paper, numerical analyses for three different inlet conditions - fa-field inlet boundary condition, inlet boundary condition with a linear nozzle and inlet boundary condition with a converging-diverging nozzle - have been performed and compared with experimental results to solve the problem. It is found that the inlet condition with a linear nozzle or a converging-diverging nozzle can prevent changing of inlet boundary condition, and thus predict more accurately the supersonic flow within turbine cascade than a far-field inlet boundary condition does.

• Proceedings of the Acoustical Society of Korea Conference
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• 1996.06a
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• pp.59-62
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• 1996

A numerical study of a two-dimensional acoustic field is carride ort for a spinning vortex pair located neat a wall to investigate the effect of the wall from the spinning quadrupole source in unsteady vortical flows. Based on the known incompressible flow field, the perturbed compressible acoustic terms derived from the Euler equations are calculated. Non-reflecting boundary conditions on the free field and the solid boundary conditions are developed for a generalized curvilinear coordinates system to investigate the effect of a curced wall. It is concluded that the sound generated by the quadrupole sources of unsteady vortical flows in the presence of a flat wall or a circular cylinder can be calculated by using the source terms of hydrodynamic flow fluctuations in both near and far acoustic fields simultaneously.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.1
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• pp.19-30
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• 2019

In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.10
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• pp.743-750
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• 2003

The equivalent source method(ESM) is used for the calculation of the internal pressure field for an enclosure which can have arbitrary boundary conditions and nay include internal objects which scatter the sound field. The advantage of using ESM is that it requires relatively low computing cost and is easy to model the internal diffracting objects. Typical ESM modeling uses two groups of equivalent source positions. One group includes the first order images of the source inside the enclosure. The Positions of the other group are usually on a spherical surface some distance outside the enclosure. The normal velocity on the surfaces of the enclosure walls is evaluated at a larger number of positions than there are equivalent sources. The sum of the squared difference between this velocity and the expected is minimized by adjusting the strength of the equivalent sources. This study is on the optimal far field sources positions when using the equivalent source method. In general, the far field sources are evenly distributed on a surface of a virtual sphere which is centered at the enclosure with a sufficiently large radius. In this study. optimal far field source locations are searched using simulated annealing method for various radii of spheres where far field sources are located. Simulation results showed that optimally located sources with adequate distance away from the enclosure center gave better result than sources with even distribution even with a smaller number of far field sources.

• Geomechanics and Engineering
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• v.24 no.5
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• pp.443-456
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• 2021

Structural design of the vertical displacements and shear strains in the earth fill (EF) dams has great importance in the structural engineering problems. Moreover, far fault earthquakes have significant seismic effects on seismic damage performance of EF dams like the near fault earthquakes. For this reason, three dimensional (3D) earthquake damage performance of Oroville dam is assessed considering different far-fault ground motions in this study. Oroville Dam was built in United States of America-California and its height is 234.7 m (770 ft.). 3D model of Oroville dam is modelled using FLAC3D software based on finite difference approach. In order to represent interaction condition between discrete surfaces, special interface elements are used between dam body and foundation. Non-reflecting seismic boundary conditions (free field and quiet) are defined to the main surfaces of the dam for the nonlinear seismic analyses. 6 different far-fault ground motions are taken into account for the full reservoir condition of Oroville dam. According to nonlinear seismic analysis results, the effects of far-fault ground motions on the nonlinear seismic settlement and shear strain behaviour of Oroville EF dam are determined and evaluated in detail. It is clearly seen that far-fault earthquakes have very significant seismic effects on the settlement-shear strain behaviour of EF dams and these earthquakes create vital important seismic damages on the swelling behaviour of dam body surface. Moreover, it is proposed that far-fault ground motions should not be ignored while modelling EF dams.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.216-221
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• 2001

The equivalent source method(ESM) is used for the calculation of the internal pressure field for an enclosure which can have arbitrary boundary conditions and may include internal objects which scatter the sound field. The advantage of using ESM is that it requires relatively low computing cost and is easy to model the internal diffracting objects. In the ESM modelling, some of the equivalent positions are chosen to be the same as the first order images of the source inside the enclosure, some are positioned on a spherical surface some distance outside the enclosure. The normal velocity on the surfaces of the enclosure walls is evaluated at a larger number of positions than there are equivalent sources. The sum of the squared difference between this velocity and the expected is minimized by adjusting the strength of the equivalent sources. This study is on the optimal equivalent source positions, the far field sources. Typically, the far field sources are evenly distributed on a surface of a virtual sphere which is centered at the enclosure with a sufficiently large radius. In this study, optimal far field source locations are searched using simulated annealing method and simulation results showed that optimally located sources gave better accuracy even with a smaller number of far field sources.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.09a
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• pp.83-90
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• 2001

The site effects of local geological conditions on seismic ground motion are performed using 2D numerical method. For the analysis, a numerical method far ground response analysis using FE-BE coupling method is developed. The total system is divided into two parts so called far field and near field. The far field is modeled by boundary element formulation using the multi-layered dynamic fundamental solution that satisfied radiational condition of wave. And this is coupled with near field modeled by finite elements. In order to verify the seismic response analysis, the results are compared with those of commercial code. As a result, it is shown that the developed method can be an efficient numerical method to solve the seismic response analysis of the site effect in 2D problem.

• Ocean Systems Engineering
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• v.13 no.2
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• pp.147-172
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• 2023

This study investigates the influence of loading and inflow conditions on tidal turbine performance from a hydrodynamic and hydroacoustic point of view. A boundary element method is utilized for the former to investigate turbine performance at various loading conditions under zero/non-zero yaw inflow. The boundary element method is selected as it has been selected, tested, and validated to be computationally efficient and accurate for marine hydrodynamic problems. Once the hydrodynamic solutions are obtained, such as the time-dependent surface pressures and periodic motion of the turbine blade, they are taken as the known noise sources for the subsequence hydroacoustic analysis based on the Ffowcs Williams-Hawkings formulation given in a form proposed by Farassat. This formulation is coupled with the boundary element method to fully consider the three-dimensional shape of the turbine and the speed of sound in the acoustic analysis. For validations, a model turbine is taken from a reference paper, and the comparison between numerical predictions and experimental data reveals satisfactory agreement in hydrodynamic performance. Importantly, this study shows that the noise patterns and sound pressure levels at both the near- and far-field are affected by different loading conditions and sensitive to the inclination imposed in the incoming flow.