• Title/Summary/Keyword: system of difference equations

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Incompressible Viscous Flow Analysis around a High-Speed Train Including Cross-Wind Effects (측풍영향을 고려한 고속전철 주위의 비압축성 점성 유동 해석)

  • Jung Y. R.;Park W. G.;Kim H. W.;Ha S. D.
    • 한국전산유체공학회:학술대회논문집
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    • 1995.10a
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    • pp.55-63
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    • 1995
  • The flow field around a high-speed train including cross-wind effects has been simulated. This study solves 3-D unsteady incompressible Navier-Stokes equations in the inertial frame using the iterative time marching scheme. The governing equations are differenced with 1st-order accurate backward difference scheme for the time derivatives, 3th-order accurate QUICK scheme for the convective terms and 2nd-order accurate central difference scheme for the viscous terms. The Marker-and-Cell concept was applied to efficiently solve continuity equation, which is differenced with 2nd-order accurate central difference scheme. The 4th-order artificial damping is added to the continuity equation for numerical stability. A C-H type of elliptic grid system is generated around a high-speed train including ground. The Baldwin-Lomax turbulent model was implemented to simulate the turbulent flows. To validate the present procedure, the flow around a high speed train at constant yaw angle of $45^{\circ}\;and\;90^{\circ}$ has been simulated. The simulation shows 3-D vortex generation in the lee corner. The flow separation is also observed around the rear of the train. It has concluded that the results of present study properly agree with physical flow phenomena.

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A FIFTH ORDER NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS

  • Chakravarthy, P. Pramod;Phaneendra, K.;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.689-706
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    • 2008
  • In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

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Optimizing and Identification of Design Parameters of a Cylindrical Hydraulic Engine Mount by an Optimization Method (최적화 기법에 의한 원통형 유체 엔진마운트의 설계변수 동정 및 최적화)

  • Ahn, Young-Kong
    • Journal of Power System Engineering
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    • v.21 no.3
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    • pp.66-73
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    • 2017
  • In order to identify the design parameters of a hydraulic engine mount with a nonlinear characteristics, an experimental method has been used generally. The method takes a considerable time and expense because of preparing an experimental apparatus, conducting a test, and analyzing results. Therefore, this paper presents a simple method to identify the design parameters of a cylindrical hydraulic engine mount, and optimize the design parameters. The physical model and mathematical equations of the mount were derived, and values of the design parameters of the mount were identified by optimization method with minimizing difference between the analytical results with the equations and the experimental results. This method is more simpler than the conventional experiment method and identify successfully the design parameters. In addition, the technique can optimize the design parameters of the mount to improves the isolation performance of the mount.

Compressible Boundary Layer Stability Analysis With Parabolized Stability Equations

  • Bing, Gao;Park, S.O.
    • 한국전산유체공학회:학술대회논문집
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    • 2006.10a
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    • pp.110-119
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    • 2006
  • An accurate and cost efficient method PSE is used for the stability analysis of 2D or 3D compressible boundary layers. A highly accurate finite difference PSE code has been developed at a general curvilinear coordinate system using an implicit marching procedure to deal with a broad range of transition predictions problems. Evolution of disturbances in compressible flat plate boundary layers are studied for free-stream Mach numbers ranging from 0 to 1.5. The effect of mean-flow nonparallelism is found to be weak on two dimensional waves and strong on three dimensional waves. The maximum amplification rate increases monotonically with Mach number. The present PSE solutions are compared with previous numerical investigations and experimental results and are found to be in good agreement.

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A Numerical Analysis of Rarefied Flow of Cylinder Using FDDO (FDDO를 이용한 실린더를 지나는 희박기체의 해석)

  • Ahn M. Y.;Chang K. S.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.05a
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    • pp.138-144
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    • 1998
  • The BGK equation, which is the kinetic model equation of Boltzmann equation, is solved using FDDO(finite difference with the discrete-ordinate method) to compute the rarefied flow of monatomic gas. Using reduced velocity distribution and discrete ordinate method, the scalar equation is transformed into a system of hyperbolic equations. High resolution ENO(Essentially Non-Oscillatory) scheme based on Harten-Yee's MFA(Modified Flux Approach) method with Strang-type explicit time integration is applied to solve the system equations. The calculated results are well compared with the experimental density field of NACA0012 airfoil, validating the developed computer code. Next. the computed results of circular cylinder flow for various Knudsen numbers are compared with the DSMC(Direct Simulation Monte Carlo) results by Vogenitz et al. The present scheme is found to be useful and efficient far the analysis of two-dimensional rarefied gas flows, especially in the transitional flow regime, when compared with the DSMC method.

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Real-Time Flood Forecasting System For the Keum River Estuary Dam(II) -System Application- (금강하구둑 홍수예경보시스템 개발(II) -시스템의 적용-)

  • 정하우;이남호;김현영;김성준
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.36 no.3
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    • pp.60-66
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    • 1994
  • This paper is to validate the proposed models for the real-time forecasting for the Keum river estuary dam such as tidal-level forecasting model, one-dimensional unsteady flood routing model, and Kalman filter models. The tidal-level forecasting model was based on semi-range and phase lag of four tidal constituents. The dynamic wave routing model was based on an implicit finite difference solution of the complete one-dimensional St. Venant equations of unsteady flow. The Kalman filter model was composed of a processing equation and adaptive filtering algorithm. The processng equations are second ordpr autoregressive model and autoregressive moving average model. Simulated results of the models were compared with field data and were reviewed.

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Navier-Stokes Analysis of Two Dimensional Cascade Flow (2차원 익렬유동의 Navier-Stokes 해석)

  • 정희택;백제현
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.2
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    • pp.313-324
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    • 1992
  • Two-dimensional Navier-Stokes code has been developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system, then mapped into a generalized body-fitted coordinate system. All direction of viscous terms are incorporated and turbulent effects are modeled using the Baldwin-Lomax algebraic model. Equation are discretized using finite difference method on the C-type grids and solved using implicit LU-ADI decomposition scheme. Calculations are made at a VKI turbine cascade flow in a transonic wind-tunnel and compared to experimental data. Present numerical scheme is shown to be in good agreement with the previous experimental results and simulates the two-dimensional viscous flow phenomena.

Dynamic response of heat and mass transfer in blood flow through stenosed bifurcated arteries

  • Charkravarty S.;Sen S.
    • Korea-Australia Rheology Journal
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    • v.17 no.2
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    • pp.47-62
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    • 2005
  • The present study deals with a mathematical model describing the dynamic response of heat and mass transfer in blood flow through bifurcated arteries under stenotic condition. The geometry of the bifurcated arterial segment possessing constrictions in both the parent and the daughter arterial lumen frequently appearing in the diseased arteries causing malfunction of the cardiovascular system, is formulated mathematically with the introduction of the suitable curvatures at the lateral junction and the flow divider. The blood flowing through the artery is treated to be Newtonian. The nonlinear unsteady flow phenomena is governed by the Navier-Stokes equations while those of heat and mass transfer are controlled by the heat conduction and the convection-diffusion equations respectively. All these equations together with the appropriate boundary conditions describing the present biomechanical problem following the radial coordinate transformation are solved numerically by adopting finite difference technique. The respective profiles of the flow field, the temperature and the concentration and their distributions as well are obtained. The influences of the stenosis, the arterial wall motion and the unsteady behaviour of the system in terms of the heat and mass transfer on the blood stream in the entire arterial segment are high­lighted through several plots presented at the end of the paper in order to illustrate the applicability of the present model under study.

Dynamic interaction analysis of actively controlled maglev vehicles and guideway girders considering nonlinear electromagnetic forces

  • Min, Dong-Ju;Lee, Jun-Seok;Kim, Moon-Young
    • Coupled systems mechanics
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    • v.1 no.1
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    • pp.39-57
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    • 2012
  • This study intends to explore dynamic interaction behaviors between actively controlled maglev vehicle and guideway girders by considering the nonlinear forms of electromagnetic force and current exactly. For this, governing equations for the maglev vehicle with ten degrees of freedom are derived by considering the nonlinear equation of electromagnetic force, surface irregularity, and the deflection of the guideway girder. Next, equations of motion of the guideway girder, based on the mode superposition method, are obtained by applying the UTM-01 control algorithm for electromagnetic suspension to make the maglev vehicle system stable. Finally, the numerical studies under various conditions are carried out to investigate the dynamic characteristics of the maglev system based on consideration of the linear and nonlinear electromagnetic forces. From numerical simulation, it is observed that the dynamic responses between nonlinear and linear analysis make little difference in the stable region. But unstable responses in nonlinear analysis under poor conditions can sometimes be obtained because the nominal air-gap is too small to control the maglev vehicle stably. However, it is demonstrated that this unstable phenomenon can be removed by making the nominal air-gap related to electromagnetic force larger. Consequently it is judged that the nonlinear analysis method considering the nonlinear equations of electromagnetic force and current can provide more realistic solutions than the linear analysis.

Estimating Forest Site Productivity and Productive Areas of Quercus acutissima and Quercus mongolica Using Environmental Variables (환경요인에 의한 상수리나무와 신갈나무의 임지생산력 및 적지 추정)

  • Shin, Man-Yong;Sung, Joo-Han;Chun, Jung-Hwa
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.14 no.2
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    • pp.89-97
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    • 2012
  • This study was conducted to estimate forest site productivity and productive areas of Quercus acutissima and Quercus mongolica using environmental factors including climatic variables. Using the data set from digital forest site map and forest climatic map, a total of 42 environmental variables were regressed on site index for developing the best site index equations for Quercus acutissima and Quercus mongolica. Five to six environmental factors by species were selected as independent variables in the best site index equations. For the site index equations, three evaluation statistics (i.e., mean difference, standard deviation of difference, and standard error of difference) were applied to the test data set for the validation of the results, The site index equations fitted well to the test data set with relatively low bias and variation. As a result, it was concluded that the site index equations by species were well capable of estimating site quality. Finally, based on the site index equations, the productive areas by species were estimated by applying GIS technique to the digital forest maps. In addition, the distribution of productive areas by species was illustrated.