• 대한기계학회논문집
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• 제17권2호
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• pp.467-474
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• 1993

Viscous flow and heat transfer phenomena in an axisymmetric cylinder which models a diesel engine have been numerically studied. In order to search for a way to minimize numerical diffusion, the effectiveness and the appropriateness of two selected numerical schemes for convective terms in the governing equations have been tested. They are Linear Upwind Difference Scheme and Hybrid Scheme. Using a standard k-.epsilon. turbulence model, the calculation has been carried out basically up to 180.deg. of crank angle. As a result, it was shown from comparison with previous experimental data that Linear Upwind Difference Scheme is less influenced than Hybrid Scheme by the numerical diffusion and it was suggested that these effects of numerical diffusion can be more significant than those due to turbulence modeling.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2005년도 학술발표회 논문집
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• pp.1063-1067
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• 2005

A second-order accuracy upwind scheme is used to investigate the run-up heights of tsunamis in the East Sea and the predicted results are compared with field observed data and results of a first-order accuracy upwind scheme, In the numerical model, the governing equations solved by the finite difference scheme are the linear shallow-water equations in deep water and nonlinear shallow-water equations in shallow water The target events is 1993 Hokktaido Nansei Oki Tsunami. The predicted results represent reasonably the run-up heights of tsunamis in the East Sea. And, The results of simulation is used to design inundation map.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• 한국수자원학회논문집
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• 제38권6호
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• pp.461-469
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• 2005

본 연구에서는 지진해일에 의하여 동해안에 발생하는 처오름을 모의하기 위하여 2차 정확도의 풍상차분기법을 사용하였으며, 그 결과는 현장관측값과 1차 정확도의 풍상차분기법의 산정 결과와 비교하였다. 수치해석 모형에서는 지배방정식으로 원해에서는 선형 천수 방정식, 근해에서는 비선형 천수방정식을 사용하였다. 대상 지진해일은 1983년 지진해일과 1993년 지진해일이다. 수치해석 결과 동해안의 처오름높이를 잘 재현하는 것으로 확인되었다. 또한, 지진해일 처오름 모의 결과를 범람도 작성에 이용할 수 있을 것으로 판단된다.

• 유체기계공업학회:학술대회논문집
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• 유체기계공업학회 2000년도 유체기계 연구개발 발표회 논문집
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• pp.285-292
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• 2000

Numerical calculation is applied to centrifugal pump at design condition by using commercial code STAR-CD and Tascflow, and these results are compared with experimental data at impeller outlet. Numerical analysis is also performed by changing turbulence model and discretization scheme at design condition using Tascflow. Turbulence model and discretization scheme used to Tascflow are k-$\epsilon$, k-$\omega$ turbulence model and upwind, modified linear profile scheme. W;th the same turbulence model and discretization scheme, two results of STAR-CD and Tascflow are very similar. But there is significant difference in numerical results near hub and shroud of impeller with different kinds of turbulent model and discretization scheme at design condition. And with k- $\omega$ turbulence model and modified linear profile scheme, it is showed that numerical results are very similar to experimental results of impeller outlet

• 한국방재학회:학술대회논문집
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• 한국방재학회 2008년도 정기총회 및 학술발표대회
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• pp.431-434
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• 2008

Pratical dispersion-correction scheme is applicated to simulate the distant propagation of tsunami. This scheme is based on the leap-frog finite difference scheme for the linear shallow-water equations. The new scheme has the advantage of using the constant spatial grid size and time step size even in area of variable depths. And this new model constructed by using the 2nd upwind scheme, dynamic linking method, and staggered grid system. This model is simulated to near Sokcho harbor about The Central East Sea Tsunami in 1983. And this result is compared to tide gage and result of former model.

• International Journal of Aeronautical and Space Sciences
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• 제3권1호
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• pp.74-85
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• 2002

The numerical experiment has been conducted to investigate the unsteady shock wave reflecting phenomena. The cell-vertex finite-volume, Roe's upwind flux difference splitting method with unstructured grid is implemented to solve unsteady Euler equations. The $4^{th}$-order Runge-Kutta method is applied for time integration. A linear reconstruction of the flux vector using the least-square method is applied to obtain the $2^{nd}$-order accuracy for the spatial derivatives. For a better resolution of the shock wave and slipline, the dynamic grid adaptation technique is adopted. The new concept of grid adaptation technique, which is much simpler than that of conventional techniques, is introduced for the current study. Three error indicators (divergence and curl of velocity, and gradient of density) are used for the grid adaptation procedure. Considering the quality of the solution and the numerical efficiency, the grid adaptation procedure was updated up to $2^{nd}$ level at every 20 time steps. For the convenience of comparison with other experimental and analytical results, the case of interaction between the straight incoming shock wave and a sharp wedge is simulated for various flow conditions. The numerical results show good agreement with other experimental and analytical results, in the shock wave reflecting structure, slipline, and the trajectory of the triple points. Some critical cases show disagreement with the analytical results, but these cases also have been proven to show hysteresis phenomena.

• 대한조선학회논문집
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• 제33권3호
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• pp.35-47
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• 1996

포텐셜을 기저로 하는 판요소법을 사용하여 자유 표면이 존재하는 유동장에서 일정 속도로 전진하는 3차원 물체의 형상을 설계하였다. 설계 방법으로는 원하는 압력 분포를 경계 조건으로 부여하고 이를 만족하는 물체 형상을 찾아내는 역해석법(inverse method)을 사용하였다. 즉, 주어진 압력으로부터 물체 표면에 분포된 법선 다이폴의 세기인 포텐셜 값을 결정하게 되며, 이는 물체 표면에 대한 Dirichlet형태의 경계 조건으로서 Green의 정리로부터 유도된 적분 방정식을 해석하게 된다. 전체 속도 포텐셜은 기본 유동인 선속에 대한 성분과 선제에 의하여 교란되는 성분으로 구성되어진다고 가정하였으며, 교란 포텐셜을 사용하여 선형화된 자유 표면 경계 조건을 적용하였다. 적분 방정식에 대한 수치 해석을 위해 물체 표면에 법선 다이폴과 Rankine 쏘오스를 분포하였으며, 자유 표면에는 Rankine 쏘오스를 분포하고 4점 유한 차분법을 사용하여 자유 표면 경계 조건이 만족되도록 하였다. 해로서 얻어지는 각 판요소에서의 Rankine 쏘오스의 세기는 가상의 유동 출입량으로서 형상 수정항으로 사용되었다. 몰수 회전 타원체의 형상 설계에 대하여 본 설계법을 적용한 결과 무한 수심에서나 조파 상태에서 $4{\sim}6$회의 반복 계산으로 충분히 수렴된 해를 얻을 수 있었다. 또한 자유 표면을 가르고 전진하는 Wigley 수학적 선형에 대한 형상 설계를 수행하여 만족스러운 결과를 얻어내었으며, 얻어진 수치해는 매우 안정적이고 빠른 수렴성을 보였다. 선형의 우열 비교를 통해 조파 저항을 감소시킬 수 있는 압력 분포의 형태를 파악하였으며, 이를 바탕으로 조파 저항의 관점에서의 5500TEU급 콘테이너 운반선의 설계를 수행하였다. 설계되어진 새로운 선형은 조파 저항의 관점에서 기존의 선형보다 계산과 실험에서 모두 우수하게 개량된 것으로 나타났다.