• 제목/요약/키워드: system of difference equations

검색결과 362건 처리시간 0.025초

Visualization for Fluid Dynamics Education

  • Fujii Kozo
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 1995년도 창립기념학술대회
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    • pp.38-43
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    • 1995
  • Effect of visualization as a tool for the education of fluid dynamics is mainly discussed. Visualized images are much more understandable compared to the explanation using equations and texts. Several examples are presented to clarify this statement. Then, the software system for teaching fluid dynamics using the results by the numerical simulation is discussed. Two important issues on what is needed in the system are given. First, such systems should be capable of animating images. Second, such systems should be interactively used by students. Changing parameters, coefficients, equations, etc. themselves and watching the difference are important for them to understand the nature of physics underlying the equations. The teaching system with visualization is no doubt a good tool for introducing fluid dynamics.

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다기통 엔진 흡기시스템의 유동해석 모델개발 (Development of a numerical flow model for the multi-cylinder engine intake system)

  • 송재원;성낙원
    • 대한기계학회논문집B
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    • 제20권6호
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    • pp.1921-1930
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    • 1996
  • To design an optimum engine intake system, a flow model for the intake manifold was developed by the finite difference method. The flow in the intake manifold was one-dimensional, and the finite difference equations were derived from governing equations of flow, continuity, momentum and energy. The thermodynamic properties of the cylinder were found by the first law of thermodynamics, and the boundary conditions were formulated using steady flow model. By comparing the calculated results with experimental data, the appropriate boundary conditions and convergence limits for the flow model were established. From this model, the optimum manifold lengths at different engine operating conditions were investigated. The optimum manifold length became shorter when the engine speeds were increased. The effect of intake valve timings on inlet air mass was also studied by this model. Advancing intake valve opening decreased inlet air mass slightly, and the optimum intake valve closing was found. The difference in inlet air mass between cylinders was very small in this engine.

유동계 내 집속체의 과도적 거동에 따른 출력 불균제 해석 (Analysis of Output Irregularity from the Transient Behavior of Bundle in a Flow Field)

  • 허유;김종성
    • 한국정밀공학회:학술대회논문집
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    • 한국정밀공학회 2005년도 춘계학술대회 논문집
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    • pp.965-968
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    • 2005
  • Roll drafting operation causes variations in the linear density of bundles because the bundle flow cannot be controlled completely by roll pairs. Defects occurring in this operation bring about many problems successively in the next processes. In this paper, we attempt to analyze the draft dynamics and the linear density irregularity based on the governing equation of a bundle motion that has been suggested in our previous studies. For analyzing the dynamic characteristics of the roll drafting operation, it is indispensable to investigate a transient state in time domain before the bundle flux reaches a steady state. However, since governing equations of bundle flow consisting of continuity and motion equations turn out to be nonlinear, and coupled between variables, the solutions for a transient state cannot be obtained by an analytical method. Therefore, we use the Finite Difference Method(FDM), particularly, the FTBS(Forward-Time Backward-Space) difference method. Then, the total equations system yields to an algebraic equations system and is solved under given initial and boundary conditions in an iterative fashion. From the simulation results, we confirm that state variables show different behavior in the transient state; e.g., the velocity distribution in the flow field changes more quickly the linear density distribution. During a transient flow in a drafting zone, the output irregularity is influenced differently by the disturbances, e.g., the variation in input bundle thickness, the drafting speed, and the draft ratio.

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On the Dynamics of Multi-Dimensional Lotka-Volterra Equations

  • Abe, Jun;Matsuoka, Taiju;Kunimatsu, Noboru
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2004년도 ICCAS
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    • pp.1623-1628
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    • 2004
  • In the 3-dimensional cyclic Lotka-Volterra equations, we show the solution on the invariant hyperplane. In addition, we show the existence of the invariant hyperplane by the center manifold theorem under the some conditions. With this result, we can lead the hyperplane of the n-dimensional cyclic Lotka-Volterra equaions. In other section, we study the 3- or 4-dimensional Hamiltonian Lotka-Volterra equations which satisfy the Jacobi identity. We analyze the solution of the Hamiltonian Lotka- Volterra equations with the functions called the split Liapunov functions by [4], [5] since they provide the Liapunov functions for each region separated by the invariant hyperplane. In the cyclic Lotka-Volterra equations, the role of the Liapunov functions is the same in the odd and even dimension. However, in the Hamiltonian Lotka-Volterra equations, we can show the difference of the role of the Liapunov function between the odd and the even dimension by the numerical calculation. In this paper, we regard the invariant hyperplane as the important item to analyze the motion of Lotka-Volterra equations and occur the chaotic orbit. Furtheremore, an example of the asymptoticaly stable and stable solution of the 3-dimensional cyclic Lotka-Volterra equations, 3- and 4-dimensional Hamiltonian equations are shown.

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쇄파의 초기단계 생성조건과 수치시뮬레이션 (Appearing Condition of Breaking Waves at Infant Stage and Numerical Simulation)

  • 곽승현
    • Journal of Advanced Marine Engineering and Technology
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    • 제33권6호
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    • pp.873-879
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    • 2009
  • The steady breakers at an infant stage are investigated through the numerical simulation. The appearing condition and characteristics of the sub-breaking waves are reviewed by analysing bow waves. The instability analysis is possibly done through the relationship between the free-surface curvature and circumferential force, which is obtained from the momentum equations. Navier-Stokes equations are solved by a finite difference method where the body-fitted coordinate system, the wall function and the advanced mesh system are invoked. The numerical result shows that the gradient of M/$U_s$ is greatly influenced by the Froude number and the decrease of M/$U_s$ indicates that the flows are unstable. Additionally flows with plunging or spilling are simulated successfully, but the application of breakers to the severely broken wave still remains to be settled in the future.

지하공간의 자연환기를 위한 태양 굴뚝 시스템의 응용 (Application of Solar Chimney System for Natural Ventilation in Underground Space)

  • 장향인;서승직
    • 한국태양에너지학회 논문집
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    • 제30권2호
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    • pp.87-95
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    • 2010
  • This study analyzed the performance of solar chimney system for natural ventilation in underground space. A mathematical model of the solar chimney was proposed in order to predict its performance under varying parameters and Korea climatic condition. Steady state heat transfer equations were set up using a energy balanced equations and solved using a inverse matrix method. Numerical simulation program to analyze system was developed by using MATLAB. As the results, the ventilation performance of the solar chimney was determined by the temperature difference of air channel and inlet, and the temperature difference was influenced by insolation, stack height and distance of air gab. Also the solar chimney system can provide $262.9m^3/h$ of annual average ventilation rate. Because seasonal differences of ventilation rate was calculated within 25%, the solar chimney system can be used for every season in Korea climatic condition. Through this study, performance of solar chimney system for natural ventilation was verified by numerical method. Consequently, the solar chimney system is proved to be effective device for natural ventilation utilizing at all times, and the additional studies should be made through the experimental method for imagineering and commercialization.

A recursive approach for mechanical system design sensitivity analysis

  • Daesung Bae
    • 한국공작기계학회논문집
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    • 제10권1호
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    • pp.101-111
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    • 2001
  • Recursive formulas have been effective in solving the equations of motion for large scale constratined mechanical sys-tems. However, derivation of the formulas has been limited to individual terms in the equations of motion, such as veloci-ty, acceleration. and generalized forces. The recursive formulas are generalized in this paper. The velocity transformation method is employed to transform the equations of motion from Cartesian to the joint spaces. Computational structure of the equations of motion in the joint space is carefully examined to classify all necessary computational operations into sev-eral categories. The generalized recursive formula for each category is then developed and applied whenever such a cate-gory of computation is encountered. Since the velocity transformation method yields the equations of motion in a compact form and computational efficiency is achieved by generalized recursive formulas, the proposed method is not only easy to implement but is also efficient. A library of generalized recursive formulas is developed to implement a dynamic analysis algorithm using backward difference.

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선수주위 쇄파현상의 수치시뮬레이션에 관한 기초연구 (A FUNDAMENTAL STUDY ON THE NUMERICAL SIMULATION OF WAVE BREAKING PHENOMENON AROUND THE FORE-BODY OF SHIP)

  • 엄태진;이영길;정광열
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 2005년도 추계 학술대회논문집
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    • pp.195-199
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    • 2005
  • Wave breaking phenomenon near the fore body of a ship is numerically simulated. The ship advance with uniform velocity in calm water. For the simulation, incompressible Navier-Stokes equations and continuity equation are adopted as governing equations. The simulation is carried out in staggered variable mesh system with finite difference method. Marker and Cell(MAC) method and Marker-Density method are employed to track the free surface. Body boundary conditions are satisfied with the adoption of porosity method and no-slip condition on the hull surface. The ship model has a wedge type fore-body, and the computational domain is an appropriate region around the fore-body. The computation results are compared with some experimental results. Also the difference of the free surface tracking methods are discussed.

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저온의 고-액상변화 모듈 용기의 배열에 따른 축냉시스템의 수치해석 (Numerical Analysis of Cold Storage System with Array of Solid-Liquid Phase Change Module)

  • 문수범
    • 해양환경안전학회지
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    • 제21권5호
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    • pp.577-582
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    • 2015
  • 본 논문은 육해상의 운송장치에 축냉시스템을 적용시키기 위한 기초 연구이다. 또한, 축냉재의 고액상변화에 대한 수치해석을 수행한 연구이다. 수치해석법으로는 유한차분법(Finite-Difference Method)을 이용하였으며, 1차원 비정상의 상태를 가정하여 계산하였다. 또한 용기는 직사각형의 구형용기로 가정하여 대칭의 조건을 이용하였다. 축냉을 목적으로 사용하는 열매체는 염화칼슘 수용액($CaCl_2$) 30wt%의 물성치를 사용하여 계산을 수행하였다. 계산에 영향을 미치는 요소로는 냉동고의 냉기 온도 및 냉기 유속이 있으며, 축냉재를 싸고 있는 용기는 플라스틱으로 가정하였다. 본 수치해석에서 경계층의 두께는 냉기의 속도 증가와 함께 얇게 되고 축열시간도 짧아지는 것을 확인할 수 있었다. 그리고 냉기의 유속이 빨라질수록 열전달이 촉진되어 축냉용기 전면부에서의 온도가 낮아짐을 알았다. 축냉용기의 후면부에서는 경계층이 두꺼워져 열전달이 전면부에 비해 작아짐을 알았다.

기준 좌표계에 따른 탄성체의 일반화 파랑 하중 및 응답에 대한 연구 (Investigation on the Generalized Hydrodynamic Force and Response of a Flexible Body at Different Reference Coordinate System)

  • 허경욱;최윤락
    • 대한조선학회논문집
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    • 제58권6호
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    • pp.348-357
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    • 2021
  • In this paper, the generalized hydrodynamic force and response of a flexible body are calculated at different reference coordinate systems. We generalize the equation of motion for a flexible body by using the conservation of momentum (Mei et al., 2005). To obtain the equations in the generalized mode, two different reference coordinates are adopted. The first is the body-fixed coordinate system by a rigid body motion. The other is the inertial coordinate system which has been adopted for the analysis. Using the perturbation scheme in the weakly-nonlinear assumption, the equations of motion are expanded up to second-order quantities and several second-order forces are obtained. Numerical tests are conducted for the flexible barge model in head waves and the vertical bending is only considered in the hydroelastic responses. The results show that the linear response does not have the difference between the two formulations. On the other hand, second-order quantities have different values for which the rigid body motion is relatively large. However, the total summation of second-order quantities has not shown a large difference at each reference coordinate system.