• Title/Summary/Keyword: Finite difference method (FDM)

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Development of 2DH hydrodynamic and scalar transport model based on hybrid finite volume/finite difference method (하이브리드 FVM/FDM 기반의 2차원 흐름 및 스칼라 이송 모형 개발)

  • Hwang, Sooncheol;Son, Sangyoung
    • Proceedings of the Korea Water Resources Association Conference
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    • 2021.06a
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    • pp.105-105
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    • 2021
  • 본 연구에서는 2차원 비선형 천수모형과 수심평균된 스칼라 이송모형을 해석하는 수치모형에 대해 기술하였다. 수치모형의 정확성을 보장함과 동시에 안정성을 높이기 위해 유한체적법, 플럭스 재구성 및 minmod 제한자를 사용하였다. 비선형 천수방정식의 이송항과 바닥 경사항은 계산된 수심의 양수 보존과 흐름의 정상 상태를 보장하기 위한 second order well-balanced positivity preserving central-upwind method를 이용하여 수치적으로 이산화되었다. 마찬가지로, 이송-확산 방정식 내 이송항은 동일한 2차 풍상차분법을 통해 수치적으로 풀이하였다. 격자점 경계면에서의 불연속으로 인한 수치진동을 방지하기 위해 이송항의 계산에 포함된 보존항의 차이로 인해 발생하는 스칼라의 수치확산을 최소화하기 위해 무차원의 비소산함수를 도입하였다. 또한, 확산항은 유한차분법을 이용하여 이산화하였다. 제안된 수치모형은 시간미분항의 계산을 위해 오일러 기법을 적용하여 계산된 수심 및 스칼라의 양수 보존여부와 함께 정지된 흐름의 정상 상태의 보존여부를 확인하였다. 제안된 수치모형의 해석 정확성을 평가하기 위해 1, 2차원 공간 내 다양한 흐름 조건에서의 해석해를 이용한 3개의 벤치마크 테스트를 수행하였다. 평균 제곱근 오차(Root Mean Squared Error, RMSE)를 산정하여 수치모형의 성능을 정량적으로 평가하였으며, 비소산함수를 적용함에 따라 스칼라의 수치확산이 감소하게 되었음을 확인하였다. 또한, 세 차례의 벤치마크 테스트 결과는 공통적으로 수치모형에 의해 계산된 결과값이 비소산함수를 고려함에 따라 해석해와 잘 일치함을 확인하였다.

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Option Pricing and Sensitivity Evaluation Methodology: Improvement of Speed and Accuracy (옵션 가치 및 민감도 평가 방법: 속도와 정확도 개선에 대한 고찰)

  • Choi, Young-Soo;Oh, Se-Jin;Lee, Won-Chang
    • Communications for Statistical Applications and Methods
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    • v.15 no.4
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    • pp.563-585
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    • 2008
  • This paper presents how to improve the efficiency and accuracy in the pricing and sensitivity evaluation for derivatives, since the need for the evaluation of complicated derivatives is increased. The Monte Carlo(MC) simulation using the quasi random number instead of pseudo random number can improve the elapsed time and accuracy for the valuation of European-type derivatives. However, the quasi MC simulation method has its limit for applying it in the multi-dimensional case such as American-type and path-dependent options due to the increased correlation between dimensions as the dimension of random numbers is increased. In order to complement this problem, we develop a modified method in which correlation values are controlled to be below a pre-specified value. Thus, this method is applicable for the pricing of either derivatives ill which underlying assets or risk factors are several or derivatives having path-dependent or early redemption property. Furthermore, we illustrate that it is important to take an appropriate grid interval for the use of finite difference method(FDM) by applying the FDM to one example of non-symmetrical butterfly spreads.

Numerical Investigation of Mixing Characteristics in Cavity Flow at Various Aspect Ratios (종횡비에 따른 공동형상 내부에서의 혼합특성에 관한 수치적 연구)

  • Shin, Myung Seob;Yang, Seung Deok;Yoon, Joon Yong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.39 no.1
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    • pp.79-88
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    • 2015
  • This study numerically examined the mixing characteristics of rectangular cavity flows by using the hybrid lattice Boltzmann method (HLBM) applied to the finite difference method (FDM). Multi-relaxation time was used along with a passive scalar method which assumes that two substances have the same mass and that there is no interaction. First, we studied numerical results such as the stream function, position of vortices, and velocity profile for a square cavity and rectangular cavity with an aspect ratio of 2. The data were compared with previous numerical results that have been proven to be reliable. We also studied the mixing characteristics of a rectangular cavity flow such as the concentration profile and average Sherwood number at various Pe numbers and aspect ratios.

Depleted Optical Thyristor using Vertical-Injection Structure for High Isolation Between Input and Output (완전공핍 광 싸이리스터에서 입출력의 높은 아이솔레이션을 위한 수직 입사형 구조에 관한 연구)

  • Choi Woon-Kyung;Kim Doo-Gun;Moon Yon-Tae;Kim Do-Gyun;Choi Young-Wan
    • The Transactions of the Korean Institute of Electrical Engineers C
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    • v.54 no.1
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    • pp.30-34
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    • 2005
  • This study shows the lasing characteristics of InGaAs/InGaAsP multiple-quantum-well waveguide-type depleted optical thyristor (DOT) using the vertical window. The measured switching voltage and current are 3.36 V and 10 ㎂, respectively. The lasing threshold current is 131 mA at 25 ℃. The output peak wavelength is 1570 nm at a bias current of 1.22 Ith and there is not input signal anymore in the output port. The vertical injection depleted optical thyristor - laser diode (VIDOT-LD) using the vertical-injection structure shows very good isolation between input and output signal.

Comparion of models and boundary conditions in fluid simulation of high density Inductively Coupled Plasma Sources included ion temperature equation (이온 온도 방정식이 포함된 고밀도 유도결합 플라즈마원 수송 시뮬레이션을 위한 모델 및 경계 조건 비교)

  • Kwon, Deuk-Chul;Yu, D.H.;Lee, J.K.;Yoon, N.S.;Kim, J.H.;Shin, Y.H.
    • Proceedings of the KIEE Conference
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    • 2004.07c
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    • pp.1924-1926
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    • 2004
  • 여러 그룹의 연구 결과로서 고밀도 유도결합 플라즈마원 유체 수송 시뮬레이션을 위해 다양한 경계 조건을 포함한 여러 가지 모델이 제시되어 왔다. 본 연구에서는 가능한 모델들과 경계 조건을 설정하여 FDM(finite difference method), up wind scheme, power-law scheme, die1ectric relaxation scheme[1]을 기반으로한 1차원 시뮬레이션을 통해 정확성과 수치 해석적 안정성 및 효율성 연에서 비교, 검토하였다.

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The Coupling of Conduction with Free Convection Flow Along a Vertical Flat Plate in Presence of Heat Generation

  • Taher, M.A.;Lee, Yeon-Won
    • Journal of Advanced Marine Engineering and Technology
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    • v.31 no.7
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    • pp.833-841
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    • 2007
  • The aim of this paper is to analyze the conjugate problems of heat conduction in solid walls coupled with laminar free convection flow adjacent to a vertical flat plate under boundary layer approximation. Using the similarity transformations the governing boundary layer equations for momentum and energy are reduced to a system of partial differential equations and then solved numerically using Finite Difference Method(FDM) known as the Keller-box scheme. Computed solutions to the governing equations are obtained for a wide range of non-dimensional parameters that are present in this problem, namely the coupling parameter P. the Prandtl number Pr and the heat generation parameter Q. The variations of the local heat transfer rate as well as the interface temperature and the friction along the plate and typical velocity and temperature profiles in the boundary layer are shown graphically. Numerical solutions have been consider for the Prandtl number Pr=0.70

Experimental and Finite Difference Method(FDM) Analysis on Collection Characteristics of Electrostatic Precipitator (전기집지기 집진특성 실험 및 유한차분해석에 관한 연구)

  • 김용진;홍원석;최헌오;함병훈;민춘식;유기선
    • Journal of Korean Society for Atmospheric Environment
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    • v.10 no.1
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    • pp.49-56
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    • 1994
  • Electrostatic Precipitators( EP ) are widely used in industry for controlling the emission of particulate pollutant Recently, a number of researches have been conducted to solve performance and reliability problems of EP, As a result of researches in the laboratory and of pilot scale, a technology of wide-pitch-spacing has been successfully applied to full scale units. It has been known that the wide-pitch-spacing can reduce the capital cost of newly installed precipitators, and the cost of rebuilding existing uints. In this paper, a systematic study was performed to develop a wide-pitch electrostatic precipitator. The study includes experimental and numerical work on the following : Particle collection characteristics for a bench-scale unit; gas flow characteristics( temperature and velocity distributions): other EP operating variables such as electric Power supply/control. The results are applied directly to design of wide-pitch-spacing EP and the developed numerical model was found to be a good argreement with the experimental results. The EHD simulation program is necessary to design the high efficiency EP.

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Simulation of chloride penetration into concrete structures subjected to both cyclic flexural loads and tidal effects

  • Mien, Tran Van;Stitmannaithum, Boonchai;Nawa, Toyoharu
    • Computers and Concrete
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    • v.6 no.5
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    • pp.421-435
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    • 2009
  • Chloride induced corrosion is a concern that governs the durability of concrete structures in marine environments, especially in tidal environments. During the service lives of concrete structures, internal cracks in the concrete cover may appear due to imposed loads, accelerating chloride penetration because of the simultaneous action of environmental and service structural loads. This paper investigated the effects of cyclic flexural loads on chloride diffusion characteristics of plain concretes, and proposed a model to predict the chloride penetration into plain concretes subjected to both tidal environments and different cyclic flexural load levels. Further, a new experiment was performed to verify the model. Results of the model using Finite Difference Method (FDM) showed that the durability of concretes in tidal environments was reduced as cyclic flexural load levels, SR, increased, and the modeling results fitted well with the experimental results.

반원주형 윤활홈을 갖는 저어널 베어링의 열효과에 관한 연구

  • ;Lalas, D. P.
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • 1990.06a
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    • pp.58-72
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    • 1990
  • 유체 윤활 이론에 의한 저어널 베어링의 해석은 그 적용 버위가 넓기 때문에 다양하게 연구되어왔다. 근래에는 열적 효과의 중요성 때문에, 윤활유의 점도와 온도와의 관계, 윤활유 주입홈에서의 윤활유 혼합현상, Cavitation현상, 고속에서 윤활유의 난류현상, 윤활유 주입구의 위치 그리고 경사진 베어링 축이 유막에 미치는 영향 등 다양한 연구가 활발히 진행되고 있다. 본 연구에서는 반원주형 윤활홈을 갖는 저어널 베어링의 주입 윤활유의 열효과가 베어링 부하량과 마찰에 미치는 영향 등을 고찰하였고, 본 연구를 수행하기 위해, 베어링 Bush와 Shfft벽에서 여러가지 열전달 겅계 조건을 가정한 가운데 Reynolds 방정식을 Energy 방정식과 동시에 수치해석적으로 풀었다. 수치해석 방법은 FDM(Finite Difference Method) 중 SOR(Successive Over-Relaxation)Technigue을 이용하였다. 또한 윤활유 점도와 온도의 관계는 지수함수(Exponential Function) 형태로 취했다. 주입 윤활유 온도와 압력 그리고 윤활홈의 형태 등을 변화시켜가며 베어링 성능에 미치는 영향을 조사하였다.

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Development of 3-Dimensional Simulator for a Biped Robot (이족 보행로봇의 3차원 모의실험기 개발)

  • Noh, Kyung-Kon;Kim, Jin-Geol;Huh, Uk-Youl
    • Proceedings of the KIEE Conference
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    • 2004.07d
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    • pp.2438-2440
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    • 2004
  • This study is concerned with development of 3-Dimensional simulator of a biped robot that has a prismatic balancing weight or a revolute balancing weight. The dynamic stability equation of a biped robot which have a prismatic balancing weight is conditional linear but a walking robot's stability equation with a revolute balancing weight is nonlinear. To get a stable gait of a biped robot, stabilization equations with ZMP (Zero Moment Point) are modeled as non-homogeneous second order differential equations for each balancing weight type. A trajectory of balancing weight can be directly calculated with the FDM (Finite Difference Method) solution of the linearized differential equation. In this paper, the 3-Dimensional graphic simulator is programmed to get and calculate the desired ZMP and the actual ZMP. Walking of 4 steps was simulated and verified. This balancing system will be applied to a biped humanoid robot, which consist Begs and upper body, at future work.

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