• 제목/요약/키워드: Difference equation

검색결과 2,168건 처리시간 0.036초

스풀밸브 해석에서 Navier-Stokes 방정식과 Reynolds 방정식에 의한 비교 연구 (A Comparative Study of the Navier-Stokes Equation & the Reynolds Equation in Spool Valve Analysis)

  • 홍성호;손상익;김경웅
    • Tribology and Lubricants
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    • 제28권5호
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    • pp.218-232
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    • 2012
  • In a spool valve analysis, the Reynolds equation is commonly used to investigate the lubrication characteristics. However, the validity of the Reynolds equation is questionable in a spool valve analysis because cavitation often occurs in the groove and the depth of the groove is much higher than the clearance in most cases. Therefore, the validity of the Reynolds equation in a spool valve analysis is investigated by comparing the results obtained from the Reynolds equation and the Navier-Stokes equation. Dimensionless parameters are determined from a nondimensional form of the governing equations. The differences between the lateral force, friction force, and volume flow rate (leakage) obtained by the Reynolds equation and those obtained by the Navier-Stokes equation are discussed. It is shown that there is little difference (less than 10%), except in the case of a spool valve with many grooves where no cavitation occurs in the grooves. In most cases, the Reynolds equation is effective for a spool valve analysis under a no cavitation condition.

대수층의 부정류에 관한 연구 (Unsteady Groundwater Flow in Aquifer)

  • 이정규
    • 물과 미래
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    • 제22권2호
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    • pp.233-239
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    • 1989
  • 부정류지하수 흐름에 대한 편미분방정식 Blotzmann 변환을 통하여 상미분방정식으로 변환되었으며 유한차분법을 이용하여 수치해를 구하였다. Richardson법과 차분식을 이용하여 미지초기수면구배(missing intial slope)를 구하는 새로운 방법이 제안되었다. 본 연구에서 제안된 방법으로 초기수면구배를 구하였으며 이 값들은 다른 연구결과와 비교한 바 아주 좋은 일치를 보여주었으며 또한 이 방법이 해를 구하는데 간편하고 쉬운 방법임을 보여주었다.

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NUMERICAL SIMULATION OF THE RIESZ FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

  • Zhang, H.;Liu, F.
    • Journal of applied mathematics & informatics
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    • 제26권1_2호
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    • pp.1-14
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    • 2008
  • In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and $Gr\ddot{u}nwald$-Letnikov(G-L) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

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NUMERICAL SOLUTIONS FOR SPACE FRACTIONAL DISPERSION EQUATIONS WITH NONLINEAR SOURCE TERMS

  • Choi, Hong-Won;Chung, Sang-Kwon;Lee, Yoon-Ju
    • 대한수학회보
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    • 제47권6호
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    • pp.1225-1234
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    • 2010
  • Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

AN ADAPTIVE FINITE DIFFERENCE METHOD USING FAR-FIELD BOUNDARY CONDITIONS FOR THE BLACK-SCHOLES EQUATION

  • Jeong, Darae;Ha, Taeyoung;Kim, Myoungnyoun;Shin, Jaemin;Yoon, In-Han;Kim, Junseok
    • 대한수학회보
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    • 제51권4호
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    • pp.1087-1100
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    • 2014
  • We present an accurate and efficient numerical method for solving the Black-Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid generation: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demonstrate the accuracy and efficiency of the proposed method. The results show that the computational time is reduced substantially with the accuracy being maintained.

콘크리트의 내구성 설계시 탄산화 임계깊이가 철근부식 개시시기에 미치는 영향에 관한 연구 (Effect of Carbonation Threshold Depth on the Initiation Time of Corrosion at the Concrete Durability Design)

  • 양재원;이상현;송훈;이한승
    • 한국건축시공학회:학술대회논문집
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    • 한국건축시공학회 2010년도 춘계 학술논문 발표대회 1부
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    • pp.229-230
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    • 2010
  • The Carbonation, one of the main deterioration factors of concrete, reduces capacity of members with providing rebar corrosion environment. Consequently it suggested standards of all countries of world, carbonation depth prediction equation of respective researchers and time to rebar corrosion initiation. As a result of carbonation depth prediction equation calculation, difference of time to rebar corrosion initiation is 149 years and difference of carbonation depth prediction equation is 162 years when water cement ratio is 50%. So a study on rebar corrosion with carbonation depth will need existing reliable data and verifications by experiment.

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Bi-2212 고온초전도체 튜브의 자기확산에 관한 연구 (An experimental study of magnetic diffusion in Bi-2212 High-Tc supercondutor tube)

  • 정성기;설승윤
    • 한국초전도ㆍ저온공학회논문지
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    • 제5권2호
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    • pp.66-70
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    • 2003
  • Transient magnetic diffusion process in a melt-cast Bi2Sr2CaCu20X(Bi-2212) tube was studied by experimental and numerical analyses. The transient diffusion partial differential equation is transformed into an ordinary differential equation by integral method. The penetration depth of magnetic field into a superconducting tube is obtained by solving the differential equation numerically. The results show that the penetration depth as a function of time which is somewhat different from the results by Bean's critical state model. The reason of the difference between the present results and that of Bean's model is discussed and compared in this paper. This experiment measure the magnetic flux density in the supercondutor after supply direct-current of Bi-2212 rounded by copper coil. This study was discussed of valid of a previous numerical solution which is compared by the penetrate time and the magnetic flux density difference of between the present results and the numerical solution.

연안역 구조물 주위에서의 해빈류의 수치해석에 관한 연구 (A Study on the Numerical Model of Wave Induced Current around Nearshore Structure)

  • 민병형;이상화;김인철
    • 한국해양공학회지
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    • 제5권1호
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    • pp.55-63
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    • 1991
  • This study is to predict accurately the wave induced current accuring by the radiation stress which acts as the driving force around Nearshore structure. For the wave induced current, the depth integrated and time averaged governing equation of an unsteady nonlinear form is derived from the continuity and momentum equation of an incompressible fluid. Numerical solutions are obtained by a finite difference method for the governing equation. In the vicinity of a structure, computed flow patterns show good agreement with the hydraulic experimental data. The numerical results obtained by neglecting the convective term show a large change of alongshore and offshore current.

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MULTIGRID SOLUTION OF THREE DIMENSIONAL BIHARMONIC EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS OF SECOND KIND

  • Ibrahim, S.A. Hoda;Hassan, Naglaa Ameen
    • Journal of applied mathematics & informatics
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    • 제30권1_2호
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    • pp.235-244
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    • 2012
  • In this paper, we solve the three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind using the full multigrid (FMG) algorithm. We derive a finite difference approximations for the biharmonic equation on a 18 point compact stencil. The unknown solution and its second derivatives are carried as unknowns at grid points. In the multigrid methods, we use a fourth order interpolation to producing a new intermediate unknown functions values on a finer grid, and the full weighting restriction operators to calculating the residuals at coarse grid points. A set of test problems gives excellent results.

CLASSIFICATION OF NONOSCILLATORY SOLUTIONS OF SECOND ORDER SELF-ADJOINT NEUTRAL DIFFERENCE EQUATIONS

  • Liu, Yujun;Liu, Zahaoshuang;Zhang, Zhenguo
    • Journal of applied mathematics & informatics
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    • 제14권1_2호
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    • pp.237-249
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    • 2004
  • Consider the second order self-adjoint neutral difference equation of form $\Delta(a_n$\mid$\Delta(x_n\;-\;{p_n}{x_{{\tau}_n}}$\mid$^{\alpha}sgn{\Delta}(x_n\;-\;{p_n}{x_{{\tau}_n}}\;+\;f(n,\;{x_{g_n}}\;=\;0$. In this paper, we will give the classification of nonoscillatory solutions of the above equation; and by the fixed point theorem, we present some existence results for some kinds of nonoscillatory solutions of the equation.