• Title/Summary/Keyword: 3차원 오차방정식

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Ocean Outfall Modelling with the Particle Tracking Method (입자추적법을 이용한 해양방류구 모델링)

  • Jung, Yun-Chul
    • Journal of Navigation and Port Research
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    • v.26 no.5
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    • pp.563-569
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    • 2002
  • To overcome the weaknesses of conventional finite difference model in pollutant dispersion modelling, the particle tracking method is used. In this study, a three dimensional particle tracking model which can be used in Princeton Ocean Model was developed and verified through the various numerical tests. Usability of the model was also confirmed through the ocean outfall modelling in Tampa Bay, Florida. As it is expected, random walk model showed the less dispersion in a range compared to the conventional finite difference model and its reason is estimated due to an error from numerical diffusion which the conventional model holds. This newly developed model is expected to be used in various ocean dispersion modelling.

Development of a numerical algorithm for wave modeling over complex structure in a CFD model (파랑해석 CFD 모형의 복합구조 구현을 위한 수치 알고리즘 개발)

  • Yoon, Jae Seon;Ha, Taemin
    • Proceedings of the Korea Water Resources Association Conference
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    • 2019.05a
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    • pp.281-281
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    • 2019
  • 수리모형실험은 수로 내에서 장시간 파랑을 발생시킬 경우, 수로 내에 반사 파랑의 성분이 누적될 수 있어 상당한 계측 오차를 발생시킬 우려가 있어 수리모형실험 결과의 검증이 필요하다. 일반적으로 수리모형실험 결과의 검증을 위해서는 동일 실험을 무수히 반복하여 불확실성을 제거하거나 다양한 수리실험실에서 수리모형실험을 수행하고 결과를 분석하여 불확실성을 제거할 수 있다. 그러나 이는 엄청난 시간과 노력은 물론 막대한 실험비용이 소요되기 때문에 경제적으로 효용성이 매우 낮아 현실적으로 수행이 어렵다. 이에 비해 수치모형실험은 상대적으로 저렴한 비용으로 수행할 수 있으며, 다수의 실험을 수행하지 않아도 불확실성을 제거할 수 있어 수리모형실험의 검증에 효율적이다. 일반적으로 난류 거동을 동반하는 복잡한 구조물 주변의 흐름 해석에는 3차원 CFD 모형이 필요하다. 특히, 병렬연산이 가능한 CFD 모형을 활용하면 수리모형실험에서도 재현이 쉽지 않은 다양한 조건에 따른 복잡한 흐름을 해석할 수 있어 효용성이 점점 증가하고 있다. 그러나 복잡한 구조물이 존재하게 되면 구조물에 재현에 막대한 격자구조가 필요하여 현실적으로 적용이 쉽지 않다. 이에 대한 대안으로 복잡한 구조물을 비교적 큰 격자에서 재현할 수 있는 가상경계법을 활용하는 연구가 활발히 진행되고 있다. 가상경계법은 Navier-Stokes 방정식에서 유체 내에 존재하는 고체를 모멘텀 이론으로 대체하여 고려하는 기법으로 수치모델링 수행 시 매질을 유체만으로 구성할 수 있어 안정적으로 적용할 수 있는 것으로 알려져 있다. 본 과업에서는 다양한 분야에서 널리 활용되고 있는 3차원 CFD 모형인 OpenFOAM®기반으로 파랑해석에 필요한 경계조건을 계산할 수 있는 olaFlow를 활용하여 복잡한 구조물을 지나는 파랑해석을 수행하기 위해 가상경계법을 olaFlow에 도입한 수치 알고리즘을 개발하였다. 개발한 수치알고리즘을 활용하여 복잡한 구조를 수치모델에서 재현하였으며, 수치모델에 적용된 수치 알고리즘의 안정성에 대해 고찰하였다.

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Numerical Study on the Observational Error of Sea-Surface Winds at leodo Ocean Research Station (수치해석을 이용한 이어도 종합해양과학기지의 해상풍 관측 오차 연구)

  • Yim Jin-Woo;Lee Kyung-Rok;Shim Jae-Seol;Kim Chong-Am
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.18 no.3
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    • pp.189-197
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    • 2006
  • The influence of leodo Ocean Research Station structure to surrounding atmospheric flow is carefully investigated using CFD techniques. Moreover, the validation works of computational results are performed by the comparison with the observed data of leodo Ocean Research station. In this paper, we performed 3-dimensional CAD modelling of the station, generated the grid system for numerical analysis and carried out flow analyses using Navier-Stokes equations coupled with two-equation turbulence model. For suitable free stream conditions of wind speed and direction, the interference of the research station structure on the flow field is predicted. Beside, the computational results are benchmarked by observed data to confirm the accuracy of measured date and reliable data range of each measuring position according to the wind direction. Through the results of this research, now the quantitative evaluation of the error range of interfered gauge data is possible, which is expected to be applied to provide base data of accurate sea surface wind around research stations.

Development of Three-dimensional Inversion Algorithm of Complex Resistivity Method (복소 전기비저항 3차원 역산 알고리듬 개발)

  • Son, Jeong-Sul;Shin, Seungwook;Park, Sam-Gyu
    • Geophysics and Geophysical Exploration
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    • v.24 no.4
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    • pp.180-193
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    • 2021
  • The complex resistivity method is an exploration technique that can obtain various characteristic information of underground media by measuring resistivity and phase in the frequency domain, and its utilization has recently increased. In this paper, a three-dimensional inversion algorithm for the CR data was developed to increase the utilization of this method. The Poisson equation, which can be applied when the electromagnetic coupling effect is ignored, was applied to the modeling, and the inversion algorithm was developed by modifying the existing algorithm by adopting comlex variables. In order to increase the stability of the inversion, a technique was introduced to automatically adjust the Lagrangian multiplier according to the ratio of the error vector and the model update vector. Furthermore, to compensate for the loss of data due to noisy phase data, a two-step inversion method that conducts inversion iterations using only resistivity data in the beginning and both of resistivity and phase data in the second half was developed. As a result of the experiment for the synthetic data, stable inversion results were obtained, and the validity to real data was also confirmed by applying the developed 3D inversion algorithm to the analysis of field data acquired near a hydrothermal mine.

Magnetization structure of Aogashima Island using vector magnetic anomalies obtained by a helicopter-borne magnetometer (항공 벡터 자기이상 자료를 이용한 아오가시마섬(청도)의 자화구조 연구)

  • Isezaski, Nobuhiro;Matsuo, Jun
    • Geophysics and Geophysical Exploration
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    • v.12 no.1
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    • pp.17-26
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    • 2009
  • On Aogashima Island, a volcanic island located in the southernmost part of the Izu Seven Islands Chain, vector magnetic anomalies were obtained in a helicopter-borne magnetic survey. The purpose of this study was to understand the volcanic structure of Aogashima Island in order to mitigate future disasters. Commonly, to obtain the magnetic structure of a volcanic island, total intensity anomalies (TIA) have been used, even though they have intrinsic errors that have not been evaluated correctly. Because the total intensity magnetic anomaly (TIA) is not a physical value, it does not satisfy Maxwell's Equations, Laplace's Equation, etc., and so TIA is not suitable for any physical analyses. In addition, it has been conventionally assumed that TIA is the same as the projected total intensity anomaly vector (PTA) for analyses of TIA. However, the effect of the intrinsic error ($\varepsilon_T$ = TIA.PTA) on the analysis results has not been taken into account. To avoid such an effect, vector magnetic anomalies were measured so that a reliable analysis of Aogashima Island magnetization could be carried out. In this study, we evaluated the error in TIA and used vector anomalies to avoid this erroneous effect, in the process obtaining reliable analysis results for 3D, vector magnetization distributions. An area of less than 1 A/m magnetization was found in the south-west part of Aogashima Island at the depth of 1.2 km. Taking the location of fumarolic activity into consideration, the lower-magnetization area was expected to be the source of that fumarolic activity of Aogashima Island.

Closing Analysis of Symmetric Steel Cable-stayed Bridges and Estimation of Construction Error (대칭형 강 사장교의 폐합해석과 시공오차의 예측)

  • Lee, Min Kwon;Lee, Hae Sung
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.1A
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    • pp.55-65
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    • 2006
  • This paper presents the closing analysis of a symmetric steel cable-stayed bridge erected by a free cantilever method. Two independent structural systems are formed before the closing procedure of a bridge is performed, and thus the compatibility conditions for vertical displacement and rotational angle are not satisfied at the closing section without the application of proper sectional forces. Since, however, it is usually impossible to apply sectional forces at the closing section, the compatibility conditions should be satisfied by proper external forces that can be actually applicable to a bridge. Unstrained lengths of selected cables and the pull-up force of a derrick crane are adjusted to satisfy nonlinear compatibility conditions, which are solved iteratively by the Newton-Raphson method. Cable members are modeled by the elastic catenary cable elements, and towers and main girders are discretized by linear 3-D frame elements. The sensitivities of displacement with respect to the unstrained lengths of selected cables and the pull-up force of the derrick crane are evaluated by the direct differentiation of the equilibrium equation. A Monte-Carlo simulation approach is proposed to estimate expected construction errors for a given confidence level. The proposed method is applied to the second Jindo Grand Bridge to demonstrate its validity and effectiveness.

Numerical Simulation of Liquid Sloshing in Three- Dimensional Tanks (3차원(次元) 탱크내에서의 액체(液體) 슬로싱의 수치(數値) 해석(解析))

  • J.H. Hwang;I.S. Kim;Y.S. Seol;S.C. Lee;Y.K. Chon
    • Journal of the Society of Naval Architects of Korea
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    • v.28 no.1
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    • pp.12-18
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    • 1991
  • Three-dimensional nonlinear sloshing effects due to tank motions are simulated by solving boundary value problem using the panel method based on boundary integral technique. While Shinkai used boundary elements on which source strengths vary linearly between nodes, the source of constant strength is distributed on each triangular panel in the present study. The source strength at each time step is determined by solving the Fredholm integral equation of the second kind obtained from Green's theorem. To avoid cumulative numerical errors as time elapses, Adam-Bashforth-Moulton method is employed. Numerical examples for the case of partially filled spherical tank on board oscillating in harmonic sway mode or pitch mode are solved. The elevation of the free surface is compared with the result by Shinkai and confirmed in good agreement during early time. The input and the output energy are comparatively evaluated to check the overall accuracy of the present numerical scheme. Although some leakage of energy are found as time marches, it is plausible when we take into account nonlinearities of the problem and the number of panels of the model.

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2D Fluid Modeling of Ar Plasma in a 450 mm CCP Reactor

  • Yang, Won-Gyun;Kim, Dae-Ung;Yu, Sin-Jae;Ju, Jeong-Hun
    • Proceedings of the Korean Vacuum Society Conference
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    • 2012.08a
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    • pp.267-267
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    • 2012
  • 최근 국내 반도체 장비 업체들에 의해서 차세대 반도체용 450 mm 웨이퍼 공정용 장비 개발이 진행 중에 있다. 반도체 산업은 계속해서 반도체 칩의 크기를 작게 하고, 웨이퍼 크기를 늘리면서 웨이퍼 당 칩수를 증가시켜 생산성을 향상해오고 있다. 현재 300 mm 웨이퍼에서 450 mm 웨이퍼를 도입하게 되면, 생산성 뿐만 아니라 30%의 비용절감과 50%의 cycle-time 단축이 기대되고 있다. 장비에 대한 이해와 공정에 대한 해석 능력을 위해 비용과 시간이 많이 들기 때문에 최근 컴퓨터를 활용한 수치 모델링이 진행되고 있다. 또한, 수치 모델링은 실험 결과와의 비교가 필수적이다. 본 연구에서는 450 mm 웨이퍼 공정용 장비의 전자밀도를 cut off probe를 통해 100 mTorr에 서 Ar 플라즈마를 파워에 따라 측정했다. 13.56 MHz 200 W, 500 W, 1,000 W로 입력 파워가 증가하면서 웨이퍼 중심에서 $6.0{\times}10^9#/cm^3$, $1.35{\times}10^{10}#/cm^3$, $2.4{\times}10^{10}#/cm^3$로 증가했다. 450 mm 웨이퍼 영역에서 전자 밀도의 불균일도는 각각 10.31%, 3.24%, 4.81% 였다. 또한, 이 450 mm 웨이퍼용 CCP 장비를 축대칭 2차원으로 형상화하고, 전극에 13.56 MHz를 직렬로 연결된 blocking capacitor ($1{\times}10^{-6}$ F/$m^2$)를 통해 인가할 수 있도록 상용 유체 모델 소프트웨어(CFD-ACE+, EXI corp)를 이용하여 계산하였다. 주요 전자-중성 충돌 반응으로 momentum transfer, ionization, excitation, two-step ionization을 고려했고, $Ar^+$$Ar^*$의 표면 재결합 반응은 sticking coefficient를 1로 가정했다. CFD-ACE+의 CCP 모델을 통해 Poisson 방정식을 풀어서 sheath와 wave effect를 고려하였다. Stochastic heating을 고려하지 않았을 때, 플라즈마 흡수 파워가 80 W, 160 W, 240 W에서 실험 투입 전력 200 W, 500 W, 1,000 W일 때와 유사한 반경 방향의 플라즈마 밀도 분포를 보였다. 200 W, 500 W, 1,000 W일 때의 전자밀도 분포는 수치 모델링과 전 범위에서 각각 10%, 3%, 2%의 오차를 보였다. 450 mm의 전극에 13.56 MHz의 전력을 인가할 때, 파워가 증가할수록 전자밀도의 최대값의 위치가 웨이퍼 edge에서 중심으로 이동하고 있음을 실험과 모델링을 통해 확인할 수 있었다.

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Georeferencing of Indoor Omni-Directional Images Acquired by a Rotating Line Camera (회전식 라인 카메라로 획득한 실내 전방위 영상의 지오레퍼런싱)

  • Oh, So-Jung;Lee, Im-Pyeong
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.30 no.2
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    • pp.211-221
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    • 2012
  • To utilize omni-directional images acquired by a rotating line camera for indoor spatial information services, we should register precisely the images with respect to an indoor coordinate system. In this study, we thus develop a georeferencing method to estimate the exterior orientation parameters of an omni-directional image - the position and attitude of the camera at the acquisition time. First, we derive the collinearity equations for the omni-directional image by geometrically modeling the rotating line camera. We then estimate the exterior orientation parameters using the collinearity equations with indoor control points. The experimental results from the application to real data indicate that the exterior orientation parameters is estimated with the precision of 1.4 mm and $0.05^{\circ}$ for the position and attitude, respectively. The residuals are within 3 and 10 pixels in horizontal and vertical directions, respectively. Particularly, the residuals in the vertical direction retain systematic errors mainly due to the lens distortion, which should be eliminated through a camera calibration process. Using omni-directional images georeferenced precisely with the proposed method, we can generate high resolution indoor 3D models and sophisticated augmented reality services based on the models.

The Estimation of the Uplift Pressure and Seepage Discharge under Gravity Dam: Development of a 3-D FDM Model in Heterogeneous Media (중력댐 하부 침투류에 의한 양압력과 누수량 산정 -비균질 3차원 FDM 모형의 개발 및 적용-)

  • Kim, Sang-Jun
    • Journal of Korea Water Resources Association
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    • v.46 no.12
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    • pp.1221-1234
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    • 2013
  • The purpose of this study is to suggest the methodology for the computation of uplift pressure and discharge of the seepage flow under gravity dam. A 3-dimensional FDM model is developed for this purpose and this model can simulate the saturated Darcian flow in heterogeneous media. For the verification of the numeric model, test simulation has been executed and the mass balance has been checked. The error does not exceed 3%. Using the developed model, The uplift pressure and seepage flow discharge under gravity dam has been calculated. The uplift pressure shows the similar pattern, comparing with the result of flow-net method. As the length of grout curtain increases, the uplift pressure decreases linearly, but the seepage flow discharge shows the non-linear decreasing pattern. The coefficients of the formulas in the dam-design criteria have been analysed, and ${\alpha}=1/3$ corresponds to the value when the length of curtain grout is 70% of the aquifer height. The uplift pressure near the pressure relief drain has the big curvature vertically and horizontally. The developed model in this study can be used for the evaluation of the effects of seepage flow under gravity dam.