• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.297-311
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• 2015

We present a robust and accurate boundary condition for pricing financial options that is a hybrid combination of the payoff-consistent extrapolation and the Dirichlet boundary conditions. The payoff-consistent extrapolation is an extrapolation which is based on the payoff profile. We apply the new hybrid boundary condition to the multi-dimensional Black-Scholes equations with a high correlation. Correlation terms in mixed derivatives make it more difficult to get stable numerical solutions. However, the proposed new boundary treatments guarantee the stability of the numerical solution with high correlation. To verify the excellence of the new boundary condition, we have several numerical tests such as higher dimensional problem and exotic option with nonlinear payoff. The numerical results demonstrate the robustness and accuracy of the proposed numerical scheme.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.8
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• pp.2561-2571
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• 1996

The flow in the turbomachinery is very unsteady due to the stator-rotor interaction. It has been indicated that the stator-rotor interaction has three distinct causes of unsteadiness: that is, the viscous vortex shedding, wake rotor interaction and potential stator-rotor interaction. In this paper, the mechanism of unsteady potential interaction and wake interaction in the stator-rotor stage flow is numerically investigated in two-dimensional view point. The numerical technique used is the upwind scheme of Van Leer's Flux Vector Splitting(FVS) and cubic spline interpolation is applied on zonal interface. Then, the flow field of a compressor stage composed of NACA 65410 is analyzed. Flow fields are found to be simulated reasonably by this method and the sensitivity due to back-pressure variation is more stronger than rotor-velocity variation.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.11
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• pp.1371-1378
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• 1999

Flow through turbomachinery has a very complex structure and Is Intrinsically unsteady. In addition, trend to highly loaded turbomachinery makes the flow extremely complex due to the interaction between rotor and stator. In this study, flows through UTRC LSRR turbine are numerically analyzed using 2 dimensional Navier-Stokes equations. The convective terms of the governing equations are discretized using the Van-Leer's FVS(Flux vector splitting) with an upwind TVD scheme. The conventional central differencing is used to discretize the diffusion terms on the finite volume. The accurate unsteady motion is achieved by using a 2nd order accurate, 3-point Euler implicit scheme. The quasi-conservative zonal scheme is used for calculating the flow variables on the zonal interface between the rotor and stator. The axial gap between stator and rotor has been configured in two variations, 15% and 65% of average chord length. The analysis program is validated using experimental results and the effect of axial gap is examined. The numerical analysis results are presented by time averaged pressure coefficient and pressure magnitude coefficient and compared with experimental results.

• Atmosphere
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• v.18 no.3
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• pp.207-224
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• 2008

Severe downslope windstorms observed at Gangneung, Korea in the springtime during the last 30 years are studied to understand their generation mechanisms. 92 severe wind cases are selected for which the maximum instantaneous wind speeds exceed two standard deviation of total mean plus ($18.7ms^{-1}$). They are categorized into the three mechanisms (hydraulic jump, partial reflection, and critical-level reflection) proposed in previous studies based on the flow condition, which is calculated using the wind and temperature profile observed at one upstream rawinsonde station, Osan. Among the three, partial reflection is found to be the most frequent mechanism for the last 30 years (1976 - 2005). To understand the role of inversion in generating severe downslope windstorms, horizontal velocity perturbation was calculated analytically for the atmosphere with an inversion layer. It turned out that the intensity of downslope wind was increased by inversion layer of specific heights, which are well matched with the observations. For better understanding the generation mechanisms, two-dimensional numerical simulations are conducted for the 92 severe wind cases using the ARPS model. In most simulations, surface wind speed exceeds the value of the severe-wind criterion, and each simulated case can be explained by its own generation mechanism. However, in most simulations, the simulated surface wind speed is larger than the observed, due to ignoring the flow-splitting effect in the two-dimensional framework.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.389-396
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• 2010

In this paper, a new computational code was developed using Chorin's artificial compressibility method to solve the two-dimensional incompressible Navier-Stokes equations. In spatial derivatives, Roe's flux difference splitting was used for the inviscid flux, while central differencing was used for the viscous flux. Furthermore, AF-ADI with dual time stepping method was implemented for accurate unsteady computations. Two-equation turbulence models, Menter's $k-{\omega}$ SST model and Coakley's $q-{\omega}$ model, hae been adopted to solve high-Reynolds number flows. A number of numerical simulations were carried out for steady laminar and turbulent flow problems as well as unsteady flow problem. The code was verified and validated by comparing the results with other computational results and experimental results. The results of numerical simulations showed that the present developed code with the artificial compressibility method can be applied to slve steady and unsteady incompressible flows.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.6 s.237
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• pp.904-912
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• 2005

The flow in a microchannel is usually characterized as a low Reynolds number (Re) so that good mixing is quite difficult to be achieved. In this regard, we developed a novel chaotic micromixer, named Barrier Embedded Kenics Micromixer (BEKM). In the BEKM, the higher level of chaotic mixing can be achieved by combining two general chaotic mixing mechanisms: (i) splitting/reorientation by helical elements inside the microchannel and (ii) stretching/folding via periodically located barriers on the channel wall. The fully three-dimensional geometry of BEKM was realized by a micro-stereolithography technology, in this study, along with a Kenics micromixer and a circular T-pipe. Mixing performances of three micromixers were experimentally characterized in terms of an average mixing color intensity of phenolphthalein. Experimental results show that BEKM has better mixing performance than other two micromixers. Chaotic mixing mechanism, proposed in this study, could be integrated as a mixing component with Micro-Total-Analysis-System, Lab-on-a-chip and so on.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1518-1526
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• 2001

In this paper, the mechanism of unsteady potential interaction and wake interaction in one stage axial turbine is numerically investigated at design point in two-dimensional viewpoint. The numerical technique used is the upwind scheme of Van-Leer's Flux Vector Splitting (FVS) and Cubic spline interpolation is applied on zonal interface between stator and rotor. The inviscid analysis is used to embody the influence of potential interaction only and viscous analysis is used to embody the influences of both potential interaction and wake interaction at the same time. The potential-flow disturbance from the stator into a rotor passage and the periodic blockage effect of rotor produce the unsteady pressure on the blade surface in inviscid analysis. After the wake is cut by rotor, two counterrotating votical patterns flanking the wake centerline in the passage are generated. So, these phenomena magnify the unsteady pressure in viscous analysis than that in inviscid analysis. The resulting unsteady forces on the rotor, generated by the combined interaction of the two effects by potential and wake interaction, are discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.10
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• pp.1384-1391
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• 2001

Three-dimensional flow analysis is implemented to investigate the flow through transonic axial-flow compressor rotor(NASA R67) and to evaluate the performances of Abid's low-Reynolds-number k-$\omega$ and Baldwin-Lomax turbulence models. A finite volume method is used fur spatial discretization. The equations are solved implicitly in time by the use of approximate factorization. The upwind difference scheme is used for inviscid terms and viscous terms are approximated with central difference. The flux-difference-splitting method of Roe is used to obtain fluxes at the cell faces. Numerical analysis is performed near peak efficiency and near stall. The results are compared with the experimental data for NASA R67 rotor. Blade-to-Blade Mach number distributions are compared to confirm the accuracy of the code. From the results, it is concluded that Abid'k-$\omega$ model is better for the calculation of flow rate and efficiency than Baldwin-Lomax model. But, the predictions for Mach number and shock structure are almost the same.

• Proceedings of the KOSOMBE Conference
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• v.1998 no.11
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• pp.287-288
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• 1998

The virtual surgery of Artificial Heart has focused on the simple fitting trial. But, as the processes of heart surgery being complex and detail, the requests of virtual surgery become more complex. One of the complex requests is volume editing. It may contain various editing functions: 3-dimensional cutting, registration, merging, splitting, inserting, deleting, translation and deformation. We have designed and implemented 3-dimensional volume editor that can be operated in Windows NT platform. With the results of this research, we can get convenient tools for the total virtual surgery system.

• Water for future
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• v.27 no.2
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• pp.155-166
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• 1994

Various Eulerian-Lagrangian numerical models for the one-dimensional longitudinal dispersion equation are studied comparatively. In the model studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing adveciton and the other dispersion. The advection equation has been solved using the method of characteristics following fluid particles along the characteristic line and the results are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpolation polynomials are superior to Lagrange interpolation polynomials in reducing dissipation and dispersion errors in the simulation.