• Title/Summary/Keyword: Predictor-Corrector

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Numerical Simulation of Wind Induced Circulation in a Thermally Stratified Flow (수온성층흐름에서 바람에 의해 발생하는 순환흐름해석)

  • Lee, Jin Woo;Cho, Yong-Sik
    • 한국방재학회:학술대회논문집
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    • 2011.02a
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    • pp.44-44
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    • 2011
  • 저수지와 같은 갇혀진 수체는 상류에서 유입되는 오염물질 뿐만 아니라 성층현상에 의해서도 오염될 수 있다. 안정된 성층은 혐기성 조건을 제공하여 바닥에서의 과도한 조류성장을 유발하고 연직순환흐름을 방해한다. 갇혀진 수체에서의 연직순환은 환경적인 문제를 감소시킬 수 있도록 중요한 역할을 한다. 갇혀진 수체에서의 연직순환은 이러한 오염을 줄이는데 중요한 역할을 하는데, 연직순환을 일으키는 인자로는 빛의 입사, 바람, 물의 온도 및 열의 확산 등이 있으며, 그중에서도 가장 중요한 것은 바람의 영향이다. 그러므로 성층화된 흐름에서 바람에 의해 발생하는 연직순환에 대한 수치모형을 개발하고 적용하는 것이 필요하다. 본 연구에서는 수온성층흐름에서의 순환흐름을 해석하기 위하여 유속성분을 계산하고 자유수면 변위와 온도, 염도등과 같은 스칼라양의 해석을 위해 다음과 같은 3단계의 방법을 이용하였다. 첫 번째 단계(정수압 계산단계)에서는 운동량 방정식의 경사항을 음해적으로 해석하고, 두 번째 단계(자유수면 보정단계)에서는 자유수면의 변화를 계산하고 수평방향 유속성분을 계산한다. 예측-수정자 방법(predictor-corrector step method)을 이용하여 자유수면변위와 유속을 구하였다. 마지막으로 세 번째 단계(이송-확산단계)에서는 이송-확산 방정식을 이용하여 스칼라양을 계산하였다. 본 연구에서 제시한 모형의 정확도를 검증하기 위하여 정사각형수조에서 진동하는 자유수면의 해석해와 비교하였고, 성층화된 흐름에서 발생하는 연직순환에 대하여 수치모의를 실시하였다. 그 결과, 본 연구에서 개발된 수치모형이 흐름 내부의 현상을 잘 묘사함을 알 수 있었다.

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A Kalman Filter Localization Method for Mobile Robots

  • Kwon, Sang-Joo;Yang, Kwang-Woong;Park, Sang-Deok;Ryuh, Young-Sun
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.973-978
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    • 2005
  • In this paper, we investigate an improved mobile robot localization method using Kalman filter. The highlight of the paper lies in the formulation of combined Kalman filter and its application to mobile robot experiment. The combined Kalman filter is a kind of extended Kalman filter which has an extra degree of freedom in Kalman filtering recursion. It consists of the standard Kalman filter, i.e., the predictor-corrector and the perturbation estimator which reconstructs unknown dynamics in the state transition equation of mobile robot. The combined Kalman filter (CKF) enables to achieve robust localization performance of mobile robot in spite of heavy perturbation such as wheel slip and doorsill crossover which results in large odometric errors. Intrinsically, it has the property of integrating the innovation in Kalman filtering, i.e., the difference between measurement and predicted measurement and thus it is so much advantageous in compensating uncertainties which has not been reflected in the state transition model of mobile robot. After formulation of the CKF recursion equation, we show how the design parameters can be determined and how much beneficial it is through simulation and experiment for a two-wheeled mobile robot under indoor GPS measurement system composed of four ultrasonic satellites. In addition, we discuss what should be considered and what prerequisites are needed to successfully apply the proposed CKF in mobile robot localization.

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Wave propagation in a 3D fully nonlinear NWT based on MTF coupled with DZ method for the downstream boundary

  • Xu, G.;Hamouda, A.M.S.;Khoo, B.C.
    • Ocean Systems Engineering
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    • v.4 no.2
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    • pp.83-97
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    • 2014
  • Wave propagation in a three-dimensional (3D) fully nonlinear numerical wave tank (NWT) is studied based on velocity potential theory. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied to eliminate the possible saw-tooth instabilities. The artificial wave speed employed in MTF (multi-transmitting formula) approach is investigated for fully nonlinear wave problem. The numerical results from incorporating the damping zone (DZ), MTF and MTF coupled DZ (MTF+DZ) methods as radiation condition are compared with analytical solution. An effective MTF+DZ method is finally adopted to simulate the 3D linear wave, second-order wave and irregular wave propagation. It is shown that the MTF+DZ method can be used for simulating fully nonlinear wave propagation very efficiently.

Dynamic responses of a beam with breathing cracks by precise integration method

  • Cui, C.C.;He, X.S.;Lu, Z.R.;Chen, Y.M.;Liu, J.K.
    • Structural Engineering and Mechanics
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    • v.60 no.5
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    • pp.891-902
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    • 2016
  • The beam structure with breathing cracks subjected to harmonic excitations was modeled by FEM based on Euler-Bernoulli theory, and a piecewise dynamical system was deduced. The precise integration method (PIM) was employed to propose an algorithm for analyzing the dynamic responses of the deduced system. This system was first divided into linear sub-systems, between which there are switching points resulted from the breathing cracks. The inhomogeneous terms due to the external excitations were tackled by introducing auxiliary variables to express the harmonic functions, hence the sub-systems are homogeneous. The PIM was then applied to solve the homogeneous sub-systems one by one. During the procedures, a predictor-corrector algorithm was presented to determine the switching points accurately. The presented method can provide solutions with an accuracy to a magnitude of $10^{-12}$ compared with exact solutions obtained by the theories of ordinary differential equations. The PIM results are much more accurate than Newmark ones with the same time step. Moreover, it is found that the PIM can maintain a high level of accuracy even when the time step increases within a relatively wide range.

Numerical Simulation of Unsteady CH$_4$/Air Jet Diffusion Flame (비정상 CH$_4$/공기 제트 확산화염에 관한 수치모사)

  • Lee, Chang-Eon;O, Chang-Bo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.25 no.8
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    • pp.1087-1096
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    • 2001
  • The dynamic structures of unsteady CH$_4$/Air jet diffusion flame with a flame-vortex interaction were numerically investigated. A timed-dependent, axisymmetric computational model and a low mach number approximation were employed in the present calculation. A two-step global reaction mechanism which considers 6 species, was used to calculate the reaction rates. The predicted results including the gravitational effect show that the large outer vortices and the small inner vortices can be well simulated without any additional disturbances near nozzle tip. It was found that the temperature and species concentrations have deviated values even for the same mixture fraction in the flame-vortex interaction region. It was also shown that the flame surface is not deformed by the inner vortex in upstream region, while in downstream region, the flame surface is compressed or stretched by the outer vortex roll-up. The present unsteady jet flame configuration accompanying a flame-vortex interaction is expected to give good implications for the unsteady structures of turbulent flames.

Vortex-Induced Vibration of Simple Slender Structure Using Cartesian Mesh (직교격자를 이용한 단순 세장 구조물의 와유기 진동 해석)

  • Han, Myung-Ryoon;Ahn, Hyung-Teak
    • Journal of the Society of Naval Architects of Korea
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    • v.48 no.3
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    • pp.260-266
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    • 2011
  • For long slender offshore structures, such as cables and pipe lines, their interaction with surrounding fluid flow becomes an important issue for global design of ocean systems. We employ a long circular cylinder as a representative case of slender offshore structure. A flexibly mounted cylinder in cross-flow generates complex vortex shedding and results in oscillation of the structure. In this paper, flow behind a circular cylinder at Re=100 is simulated. The vortex shedding pattern and flow induced motion are examined in the cross flow configuration as well as with various yaw-angled configurations. The "Lock-in" phenomenon is also observed when reduced velocity is approximately 4.0. The MAC Grid system, which is the typical grid system for Cartesian mesh and pressure correction methods, are used for solving the incompressible Navier-Stokes equations. Predictor/Corrector method is applied for obtaining a non-linear response of structure at the flexibly mounted. The existance and motion of the body is represented by the immersed boundary technique.

Three Dimensional Finite Element Analysis of Free Surface Flow Using Filling Pattern Technique and Adaptive Grid Refinement (형상 충전 및 격자 세분화를 이용한 삼차원 자유 표면 유동의 유한 요소 해석)

  • Kim, Ki-Don;Yang, Dong-Yol;Jeong, Jun-Ho
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.28 no.11
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    • pp.1348-1358
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    • 2004
  • The filling pattern and an adaptive grid refinement based on the finite element method and Eulerian mesh advancement approach have been developed to analyze incompressible transient viscous flow with free surfaces. The governing equation fur flow analysis is Navier-Stokes equation including inertia and gravity effects. The mixed FE formulation and predictor-corrector method are used effectively for unsteady numerical simulation. The flow front surface and the volume inflow rate are calculated using the filling pattern technique to select an adequate pattern among seven filling patterns at each tetrahedral control volume. By adaptive grid refinement, the new flow field that renders better prediction in flow surface shape is generated and the velocity field at the flow front part is calculated more exactly. In this domain the elements in the surface region are made finer than those in the remaining regions for more efficient computation. The collapse of a water dam and the filling of a fluidity spiral have been analyzed. The numerical results have been in good agreement with the experimental results and the efficiency of the adaptive grid refinement and filling pattern techniques have been verified.

Numerical Analysis of Ship Motions in Beam Sea Using Unsteady RANS and Overset Grid Methods (비정상 RANS 법과 중첩격자계를 이용한 횡파중 선박운동 수치해석)

  • Park, Il-Ryong;Hosseini, Seyed Hamid Sadat;Stern, Frederick
    • Journal of the Society of Naval Architects of Korea
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    • v.45 no.2
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    • pp.109-123
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    • 2008
  • The present paper presents the CFD result for a beam wave test case. An ONR tumblehome ship model with bilge keels is used. The beam wave test is for zero forward speed and roll and heave 2DOF with wave slope $a_k=0.156$ and wavelength ${\lambda}=1.12L_{PP}$, with $L_{PP}$ the ship length. The problems is solved numerically with an unsteady Reynolds averaged Navier-Stokes approach. The free surface flow is computed using a single-phase level-set method and the motions in each time step are integrated using a predictor-corrector iteration approach which uses dynamic overset grids moving with relative ship motion. The predicted CFD results for motions and forces are compared with experimental data, showing a reasonable agreement.

Dynamic Analysis of Constrained Mechanical System Moving on a Flexible Beam Structure(I) : General Approach (유연한 보 구조물 위를 이동하는 구속 기계계의 동력학 해석(I) : 일반적인 접근법)

  • Park, Chan-Jong;Park, Tae-Won
    • Journal of the Korean Society for Precision Engineering
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    • v.17 no.11
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    • pp.165-175
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    • 2000
  • In recent years, it becomes a very important issue to consider the mechanical systems such as high-speed vehicles and railway trains moving on elastic beam structures. In this paper, a general approach, which can predict the dynamic behavior of constrained mechanical system and elastic beam structure, is proposed. Also, various supporting conditions of a foundation support are considered for the elastic beam structures. The elastic structure is assumed to be a nonuniform and linear Bernoulli-Euler beam with proportional damping effect. Combined Differential-Algebraic Equations of motion are derived using multibody dynamics theory and Finite Element Method. The proposed equations of motion can be solved numerically using generalizd coordinate partitioning method and Predictor-Corrector algorithm, which is an implicit multi-step integration method.

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Analysis of Liquid Sloshing in a Two-Dimensional Elastic Tank (구조물의 탄성을 고려한 2차원 탱크내 유동해석)

  • P.M.,Lee;S.W.,Hong;S.Y.,Hong
    • Bulletin of the Society of Naval Architects of Korea
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    • v.27 no.3
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    • pp.107-116
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    • 1990
  • The liquid sloshing in an elastic tank is a fluid-structure interaction problem. It requires nonlinear analysis to solve the complicated physics involved in the large interaction of fluid-structure, the variation of dynamic characteristics of structure due to hydrodynamic loading, and the distorsion of fluid flow due to structural vibration. In this paper a Lagrangian FEM is introduced to analyze the liquid sloshing in an elastic tank assuming that the elastic wall is one degree of freedom rigid wall. Numerical integration is performed using an implicit-explicit algorithm, which is formed by mixing the predictor-corrector method and the Runge-Kutta 4th order method. The influence of dynamic characteristics of the sloshing tank on the fluid flow is discussed. The numerical method is also applied for the simulation of the wall generated wave in the tank.

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