• 한국환경과학회지
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• 제11권12호
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• pp.1321-1326
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• 2002

A numerical model is investigated to predict a behavior of the gaseous volatile organic compounds and a subsurface contamination caused by them in the unsaturated zone. Two dimensional advective-dispersion equation caused by a density difference and two dimensional diffusion equation are computed by a finite difference method in the numerical model. A laboratory experiment is also carried out to compare the results of the numerical model. The dimensions of the experimental plume are 1.2m in length, 0.5m in height, and 0.05m in thickness. In comparing the result of 2 methods used in the numerical model with the one of the experiment respectively, the one of the advective-dispersion equation shows better than the one the diffusion equation.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.269-282
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• 2007

In this paper, we consider a two-dimensional fractional space-time diffusion equation (2DFSTDE) on a finite domain. We examine an implicit difference approximation to solve the 2DFSTDE. Stability and convergence of the method are discussed. Some numerical examples are presented to show the application of the present technique.

• 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.

• 한국방재학회:학술대회논문집
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• 한국방재학회 2007년도 정기총회 및 학술발표대회
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• pp.177-180
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• 2007

Numerical simulations on the suspended load in the Do jang fish port are carried out. Suspended load is analysed by using the two-dimensional advection-diffusion equation. To describe behaviors of a pollutant in costal zone, a split-operator method is applied to the numerical model. The advection part is first solved by SOWMAC and then the diffusion part is solved by a three-level locally implicit scheme.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1125-1134
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• 2017

In this paper, we present a new multilevel in space and energy diffusion (MSED) method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1) a grey (one-group) diffusion equation used to efficiently converge the fission source and eigenvalue, (2) a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3) a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.

• Nuclear Engineering and Technology
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• 제32권6호
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• pp.605-617
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• 2000

Nodal transport methods are studied for the solution of two dimensional discrete-ordinates, simplified even-parity transport equation(SEP) which is known to be an approximation to the true transport equation. The polynomial expansion nodal method(PEN) and the analytic function expansion nodal method(AFEN）which have been developed for the diffusion theory are used for the solution of the discrete-ordinates form of SEP equation. Our study shows that while the PEN method in diffusion theory can directly be converted without complication, the AFEN method requires a theoretical modification due to the nonhomogeneous property of the transport equation. The numerical results show that the proposed two methods work well with the SEP transport equation with higher accuracies compared with the conventional finite difference method.

• Interaction and multiscale mechanics
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• 제1권3호
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• pp.369-379
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• 2008

A combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material. A corresponding Fokker-Planck continuity equation is formulated, and the interplay/competition of stochastic and curvature-driven mechanisms is investigated. Finite difference results show that the stochastic diffusion coefficient has a strong effect on the growth of small grains in the early stage in both two-dimensional columnar and three-dimensional grain systems, and the corresponding growth exponents are ~0.33 and ~0.25, respectively. With the increase in grain size, the deterministic curvature-driven mechanism becomes dominant and the growth exponent is close to 0.5. The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J $m^{-2}$ in two- and three-dimensional systems, respectively. The grain size distribution of a three-dimensional system changes dramatically with increasing time, while it changes a little in a two-dimensional system. The grain size distribution from the combined model is consistent with experimental data available.

• Bulletin of the Korean Chemical Society
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• 제12권6호
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• pp.692-698
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• 1991

The reaction path Smoluchowski equation approach developed in a recent work to calculate the rate constant for a diffusive multidimensional barrier crossing process is extended to incorporate the configuration-dependent diffusion matrix. The resulting formalism is then applied to the investigation of stilbene photoisomerization dynamics. Adapting a model two-dimensional potential and a model diffusion matrix proposed by Agmon and Kosloff [J. Phys. Chem.,91 (1987) 1988], we derive an eigenvalue equlation for the relaxation rate constant of the stilbene photoisomerization. This eigenvalue equation is solved numerically by using the finite element method. The advantages and limitations of the present method are discussed.

• Nuclear Engineering and Technology
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• 제14권4호
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• pp.178-185
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• 1982

중성자 다군 확산 방정식의 해를 구하기 위하여 albedo형 경계조건을 Hermite 3차 다항식에 의거한 유한요소법과 결합하였다. 중성자 확산문제에 흔히 이용되는 확산방정식의 weak form을 경계조건과 일치하도록 수정하였으며 또한 경계면에 접한 node영역에서의 요소함수 또한 수정 정의하였다. 수정된 유한요소법의 수치계산상의 효율성을 조사할 목적으로 2차원 ZION 가압경수형 원자로문제를 시험계산하고 그 결과를 기존의 다른 계산결과와 비교하였다.

• Nuclear Engineering and Technology
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• 제51권5호
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• pp.1181-1194
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• 2019

A new moving-mesh Finite Volume Method (FVM) for the efficient solution of the two-dimensional neutron diffusion equation is introduced. Many other moving-mesh methods developed to solve the neutron diffusion problems use a relatively large number of sophisticated mathematical equations, and so suffer from a significant complexity of mathematical calculations. In this study, the proposed method is formulated based on simple mathematical algebraic equations that enable an efficient mesh movement and CV deformation for using in practical nuclear reactor applications. Accordingly, a computational framework relying on a new moving-mesh FVM is introduced to efficiently distribute the meshes and deform the CVs in regions with high gradient variations of reactor power. These regions of interest are very important in the neutronic assessment of the nuclear reactors and accordingly, a higher accuracy of the power densities is required to be obtained. The accuracy, execution time and finally visual comparison of the proposed method comprehensively investigated and discussed for three different benchmark problems. The results all indicated a higher accuracy of the proposed method in comparison with the conventional fixed-mesh FVM.