• 제목/요약/키워드: Diffusion equation

검색결과 888건 처리시간 0.035초

A Boundary Integral Equation Formulation for an Unsteady Anisotropic-Diffusion Convection Equation of Exponentially Variable Coefficients and Compressible Flow

  • Azis, Mohammad Ivan
    • Kyungpook Mathematical Journal
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    • 제62권3호
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    • pp.557-581
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    • 2022
  • The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

A NOTE ON NUMERICAL APPROACHES FOR HEAT-DIFFUSION EQUATION WITH HETEROGENEOUS MEDIA AND ITS APPLICATIONS

  • Seo, Sat byul
    • East Asian mathematical journal
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    • 제35권1호
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    • pp.99-108
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    • 2019
  • In this paper, we introduce a numerical approach to solve heat-diffusion equation with discontinuous diffusion coefficients in the three dimensional rectangular domain. First, we study the support operator method and suggest a new method, the continuous velocity method. Further, we apply both methods to a diffusion process for neurotransmitter release in an individual synapse and compare their results.

Diffusion synthetic acceleration with the fine mesh rebalance of the subcell balance method with tetrahedral meshes for SN transport calculations

  • Muhammad, Habib;Hong, Ser Gi
    • Nuclear Engineering and Technology
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    • 제52권3호
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    • pp.485-498
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    • 2020
  • A diffusion synthetic acceleration (DSA) technique for the SN transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB) on unstructured tetrahedral meshes is presented. The LDEM-SCB scheme solves the transport equation with the discrete ordinates method by using the subcell balances and linear discontinuous expansion of the flux. Discretized DSA equations are derived by consistently discretizing the continuous diffusion equation with the LDEM-SCB method, however, the discretized diffusion equations are not fully consistent with the discretized transport equations. In addition, a fine mesh rebalance (FMR) method is devised to accelerate the discretized diffusion equation coupled with the preconditioned conjugate gradient (CG) method. The DSA method is applied to various test problems to show its effectiveness in speeding up the iterative convergence of the transport equation. The results show that the DSA method gives small spectral radii for the tetrahedral meshes having various minimum aspect ratios even in highly scattering dominant mediums for the homogeneous test problems. The numerical tests for the homogeneous and heterogeneous problems show that DSA with FMR (with preconditioned CG) gives significantly higher speedups and robustness than the one with the Gauss-Seidel-like iteration.

TRANSFORMATION OF DIMENSIONLESS HEAT DIFFUSION EQUATION FOR THE SOLUTION OF DYNAMIC DOMAIN IN PHASE CHANGE PROBLEMS

  • Ashraf, Muhammad;Avila, R.;Raza, S. S.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제13권1호
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    • pp.31-40
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    • 2009
  • In the present work transformation of dimensionless heat diffusion equation for the solution of moving boundary problems have been formulated. The formulation is based on 1-D, 2-D and 3-D, unsteady heat diffusion equations. These equations are rst turned int dimensionless form by using dimensionless quantities and their transformation was formulated in liquid and solid phases. The salient feature of this work is that during the transformation of dimensionless heat diffusion equation there arises a convective term $\tilde{v}$ which is responsible for the motion of interface in liquid as well as solid phase. In the transformed heat equation, a correction factor $\beta$ also arises naturally which gives the correct transformed flux at interface.

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THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION WITH CAPUTO DERIVATIVES

  • HUANG F.;LIU F.
    • Journal of applied mathematics & informatics
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    • 제19권1_2호
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    • pp.179-190
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    • 2005
  • We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

Smagorinsky method와 2-level method를 이용한 난류 확산계수의 비교 연구 (Comparison study of turbulent diffusion coefficient using Smagorinsky method and 2-level method)

  • 이화운;오은주;정우식;최현정;임주연
    • 한국환경과학회지
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    • 제11권7호
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    • pp.679-686
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    • 2002
  • Turbulence greatly influence on atmospheric flow field. In the atmosphere, turbulence is represented as turbulent diffusion coefficients. To estimate turbulent diffusion coefficients in previous studies, it has been used constants or 2-level method which divides surface layer and Ekman layer. In this study, it was introduced Smagorinsky method which estimates turbulent diffusion coefficient not to divide the layer but to continue in vertical direction. We simulated 3-D flow model and TKE equation applied turbulent diffusion coefficients using two methods, respectively. Then we showed the values of TKE and the condition of each term to TKE. The results of Smagorinsky method were reasonable. But the results of 2-level method were not reasonable. Therefor, it had better use Smagorinsky method to estimate turbulent diffusion coefficients. We are expected that if it is developed better TKE equation and model with study of computational method in several turbulent diffusion coefficients for reasonably turbulent diffusion, we will able to predict precise wind field and movements of air pollutants.

3차원 이방성확산 방정식을 이용한 동영상의 영상잡음제거 (Noise removal or video sequences with ,3-D anisotropic diffusion equation)

  • 이석호;최은철;강문기
    • 대한전자공학회논문지SP
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    • 제39권2호
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    • pp.79-86
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    • 2002
  • 최근에 확산방정식을 영상처리에 응용하는 연구가 세계적으로 활발하다. 특히 이방성확산 방정식은 영상에서 잡음을 제거하면서도 경계선을 강화시키는 성질로 인하여 영상잡음제거의 알고리즘으로 각광을 받고있다. 그러나 2차원 이방성확산방정식을 그대로 동영상의 영상잡음제거에 적용할 경우, 각 프레임간의 밝기 차로 인한 깜빡임 현상(flickering artifact)과 프레임간 필터링으로 인한 고스트 현상(ghost artifact)이 나타난다 그러므로 본 논문에서는 2차원 이방성확산방정식을 시퀀스 축으로 확장시킨 3차원 이방성확산방정식을 제안한다. 제안한 3차원 이방성확산방정식은 2차원 이방성확산방정식보다 더 효율적으로 영상잡음을 제거할 뿐만 아니라, 깜빡임 현상과 고스트 현상도 효율적으로 제거한다는 것을 이론적으로 그리고 실험적으로 검증하였다.

BIFURCATIONS IN A DISCRETE NONLINEAR DIFFUSION EQUATION

  • Kim, Yong-In
    • 대한수학회보
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    • 제35권4호
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    • pp.689-700
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    • 1998
  • We consider an infinite dimensional dynamical system what is called Lattice Dynamical System given by a discrete nonlinear diffusion equation. By assuming the nonlinearity to be a general nonlinear function with mild restrictions, we show that as the diffusion parameter changes the stationery state of the given system undergoes bifurcations from the zero state to a bounded invariant set or a 3- or 4-periodic state in the global phase space of the given system according to the values of the coefficients of the linear part of the given nonlinearity.

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수분확산(水分擴散)의 활성화(活性化)에너지 모델 (A Model for Activation Energy of Moisture Diffusion in Wood)

  • 강호양
    • Journal of the Korean Wood Science and Technology
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    • 제20권4호
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    • pp.21-30
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    • 1992
  • An activation energy equation for moisture diffusion in wood was developed with an assumption that activation energy is directly proportional to wood specific gravity. Theoretical activation energies obtained from the activation energy equation were revealed to be always lower than actual activation energies, which implies that activation energy isn't affected only by wood specific gravity. The other affecting factors are possibly anatomical structures of wood which determine a ratio of vapor diffusion to bound water diffusion in wood. For the convenience of estimating actual activation energy by using the activation energy equation, thirteen kinds of species were categorized into three groups according to their anatomical structures.

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