• Title/Summary/Keyword: system of elliptic equations

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Fuzzy Reasoning on Computational Fluid Dynamics - Feasibility of Fuzzy Control for Iterative Method - (CFD에로의 Fuzzy 추론 응용에 관한 연구 - 반복계산을 위한 퍼지제어의 유효성 -)

  • Lee, Y.W.;Jeong, Y.O.;Park, W.C.;Lee, D.H.;Bae, D.S.
    • Journal of Power System Engineering
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    • v.2 no.3
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    • pp.21-26
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    • 1998
  • Numerical simulations for various fluid flows require enormous computing time during iterations. In order to solve this problem, several techniques have been proposed. A SOR method is one of the effective methods for solving elliptic equations. However, it is very difficult to find the optimum relaxation factor, the value of this factor for practical problems used to be estimated on the basis of expertise. In this paper, the implication of the relaxation factor are translated into fuzzy control rules on the basis of the expertise of numerical analysers, and fuzzy controller incorporated into a numerical algorithm. From two cases of study, Poisson equation and cavity flow problem, we confirmed the possibility of computational acceleration with fuzzy logic and qualitative reasoning in numerical simulations. Numerical experiments with the fuzzy controller resulted in generating a good performance.

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Grid Generation about Full Aircraft Configuration Using Interactive Grid Generator (상호 대화형 격자생성 환경을 이용한 항공기 전기체 격자계 생성)

  • Kim Y. S.;Kwon J. H.
    • 한국전산유체공학회:학술대회논문집
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    • 1999.11a
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    • pp.145-151
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    • 1999
  • An Interactive grid generation program(KGRID) with graphical user interface(GUI) has been improved. KGRID works on the UNLX environment and GUI has been implemented with OSF/Motif and X Toolkit and the graphics language is Open GL for visualization of the 3D objects. It supports more convenient user environment to generate 2D and 3D multi-block structured grid systems. It provides various useful field grid generation methods, which are the algebraic methods, the elliptic partial differential equations method and the predictor-corrector method. It also supports 3D surface grid generation with NURBS(Non-Uniform Rational B-Spline) and various stretching functions to control grid points distribution on curves and surfaces. And some menus are added to perform flexible management, for the objects. We generated surface and field grid system about full aircraft configuration using KGRID. The performance and stability of the KGRID is verified through the generation of the grid system about a complex shape.

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Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

  • Cho, Dae Seung;Vladimir, Nikola;Choi, Tae Muk
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.5 no.3
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    • pp.478-491
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    • 2013
  • Natural vibration analysis of plates with openings of different shape represents an important issue in naval architecture and ocean engineering applications. In this paper, a procedure for vibration analysis of plates with openings and arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The presented solution represents an extension of a procedure for natural vibration analysis of rectangular plates without openings, which has been recently presented in the literature. The effect of an opening is taken into account in an intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with rectangular, elliptic, circular as well as oval openings with various plate thicknesses and different combinations of boundary conditions. The results are compared with those obtained by the finite element method (FEM) as well as those available in the relevant literature, and very good agreement is achieved.

An Experimental Study on the Turbulence Characteristics of a Cross Jet with Respect to Cross Angle Variations (충돌분사의 충돌각 변화에 따른 난류특성의 실험적 연구)

  • 노병준;최진철;강신재
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.13 no.5
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    • pp.991-998
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    • 1989
  • This investigation was carried out for the purpose of studying the turbulent flow and mixing characteristics after collision of two jets depending upon the cross angle variations. For effectuating this experimental study, a subsonic wind tunnel and a constant temperature type two channel hot-wire anemometer system have been utilized. The jets issuing from two nozzles have same Reynolds numbers and their cross angle was variable. After collision of two jets, the cross section of the mixing flow, mean and fluctuating velocities and Reynolds stresses have been measured, and analyzed comparing them with semi-empirical equations. It was found that the nondirectional contour of the cross section agreed well with an elliptic formula and the mean velocities along the centerline had a good similarity independent of cross angle variations. The distributions of U over bar-components measured in the Y direction have a good similarity and agree well with semi-empirical equations of Hinze and Gortler. The Reynolds stresses of u'v' over bar on the Y axis show a similar distributions and their agreement with the theoretical curve is remarkable but those of u'w' over bar measured along the Z axis are randomly scattered.

Effects of Rotatory Inertia and Shear Deformation on Natural Frequencies of Arches with Variable Curvature (회전관성 및 전단변형이 변화곡률 아치의 고유진동수에 미치는 영향)

  • Oh, Sang Jin;Lee, Byoung Koo;Lee, In Won
    • Journal of Korean Society of Steel Construction
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    • v.9 no.4 s.33
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    • pp.673-682
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    • 1997
  • The main purpose of this paper is to investigate the effects of rotatory inertia and shear deformation on the natural frequencies of arches with variable curvature. The differential equations are derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. The governing equations are solved numerically for parabolic, circular and elliptic geometries with hinged-hinged, hinged-clamped and clamped-clamped end constraints. For each cases, the four lowest frequency parameters are presented as functions of the two dimensionless system parameters; the arch rise to span length ratio, and the slenderness ratio.

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Free Vibration of Stepped Horizontally Curved Members Supported by Two-Parameter Elastic Foundation (두 변수 탄성지반으로 지지된 불연속 변단면 수평 곡선부재의 자유진동)

  • Lee, Byoung Koo;Lee, Tae Eun;Ahn, Dae Soon;Kim, Mu Young
    • Journal of Korean Society of Steel Construction
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    • v.13 no.6
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    • pp.651-659
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    • 2001
  • The main purpose of this paper is to present an analytical method for free vibration of stepped horizontally curved members on two-parameter elastic foundation. The ordinary differential equations governing the free vibration of such beams are derived as non-dimensional forms including the effects of rotatory inertia and shear deformation. The governing equations are solved numerically for the circular, parabolic, sinusoidal and elliptic curved beams with hinged-hinged, hinged-clamped and clamped-clamped end constraints. As the numerical results, the lowest four natural frequency parameters are presented as the functions of various non-dimensional system parameters. Also the typical mode shapes are presented.

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Propagation and Radiation Characteristics of Elliptical Corrugated Waveguide (타원형 커루게이트 도파관의 전파 및 복사 특성)

  • 고욱희;백경훈
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.9 no.5
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    • pp.614-620
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    • 1998
  • In this paper, we analyze theoritically the propagation and radiation characteristics for elliptical corrugated waveguides. The solutions of wave equations in an elliptic cylinder system are obtained in terms of Mathieu functions of 1st and 2nd kind. The electromagnetic fields in the elliptical corrugated waveguide can be represented by series and products of angular and radial Mathieu functions. By using impedence matching at the boundary between the inner region and the slot region, characteristic equations are derived. Then the characteristic equation is solved for $HE_{11}$ mode which is dominant mode in the elliptical corrugated waveguide and the fields in the aperture is calculated. And the propagation pattern for the elliptical corrugated waveguides is calculated through the field equivalence principle.

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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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Parametric Study on the $LiBr-H_2O$ Absorption Process on Horizontal Tubes (수평원관상의 $LiBr-H_2O$ 흡수특성에 대한 연구)

  • Min J. K.;Choi D. H.
    • Journal of computational fluids engineering
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    • v.5 no.1
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    • pp.33-42
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    • 2000
  • The LiBr-H₂O absorption process on a horizontal tube has been analyzed numerically. The flow field, which was calculated in the authors' previous study by solving the fully elliptic Navier-Stokes equations with accurate free-surface-tracking method, is used to solve the temperature and concentration distributions in the absorption film. With the assumption that the absorbent is linear, calculations have been made for various inlet temperature and flow-rate conditions. For low inlet temperature, the absorption rate is large in the upstream region but the mean temperature also increases and as a result the absorption decreases as the film flows to downstream while high-inlet-temperature case does the opposite. The difference in the absorption rate due to the inlet temperature change becomes smaller in the downstream than that in the upstream. For large flow rate, the heat transfer to the wall becomes poor due to the thick film and so does the absorption rate. The analyses have also been carried out for multiple tube arrangement and the results show that the absorption rate converges after a few tube rows.

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A Numerical Analysis of Free Surface Wave around a ship (선체주위 자유수면파의 수치해석)

  • Choon-Bum Hong;Seung-Hee Lee
    • Journal of the Society of Naval Architects of Korea
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    • v.31 no.3
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    • pp.80-86
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    • 1994
  • A numerical method for simulations of inviscid incompressible flow fields around a ship advancing on the free surface is developed. A body fitted coordinate system, generated by numerically solving elliptic type partial differential equations is used to conform the ship and free surface configurations. Three dimensional Euler equations transformed to the non-staggered body fitted coordinate system are discretised by finite difference method. Time and spatial derivatives are discretised by forward and centered differencings, respectively, and artificial dissipations are added to discretised convection terms for improvements of numerical stability. At each time steps, free surface elevations are recomputed to satisfy nonlinear free surface conditions. Poisson equations for pressure field are solved iteratively and the velocity field for next time step is extrapolated. To verify the developed numerical method, flow fields around a Wigley model are simulated(Fn=0.250-0.408) and compared with experimental data to show good agreements.

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