• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.629-645
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• 2020

A uniformly convergent numerical method is developed for solving singularly perturbed 1-D parabolic convection-diffusion problems. The developed method applies a non-standard finite difference method for the spatial derivative discretization and uses the implicit Runge-Kutta method for the semi-discrete scheme. The convergence of the method is analyzed, and it is shown to be first order convergent. To validate the applicability of the proposed method two model examples are considered and solved for different perturbation parameters and mesh sizes. The numerical and experimental results agree well with the theoretical findings.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1035-1054
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• 2010

We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.

• 한국반도체및디스플레이장비학회:학술대회논문집
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• 한국반도체및디스플레이장비학회 2004년도 춘계학술대회 발표 논문집
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• pp.55-58
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• 2004

This paper presents a 3-dimensional diffusion simulation with adaptive solution strategy. The developed diffusion simulator VLSIDIF-3 was designed to re-refine areas where difference of doping concentration between any of two nodes of each element is greater than tolerance and redo diffusion process until error is tolerable. Numerical experiment in low doping diffusion problem showed that this adaptive solution strategy is very efficient in both memory and time, and expected this scheme would be more powerful in complex diffusion model.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• 천문학회지
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• 제37권5호
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• pp.557-562
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• 2004

We discuss diffusion of particles in turbulent flows. In hydrodynamic turbulence, it is well known that distance between two particles imbedded in a turbulent flow exhibits a random walk behavior. The corresponding diffusion coefficient is ${\~}$ ${\upsilon}_{inj}{\iota}_{turb}$, where ${\upsilon}_{inj}$ is the amplitude of the turbulent velocity and ${\iota}_{turb}$ is the scale of the turbulent motions. It Is not clear whether or not we can use a similar expression for magnetohydrodynamic turbulence. However, numerical simulations show that mixing motions perpendicular to the local magnetic field are, up to high degree, hydrodynamical. This suggests that turbulent heat transport in magnetized turbulent fluid should be similar to that in non-magnetized one, which should have a diffusion coefficient ${\upsilon}_{inj}{\iota}_{turb}$. We review numerical simulations that support this conclusion. The application of this idea to thermal conductivity in clusters of galaxies shows that this mechanism may dominate the diffusion of heat and may be efficient enough to prevent cooling flow formation when turbulence is vigorous.

• 한국환경과학회지
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• 제6권5호
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• pp.437-449
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• 1997

To predict diffusion and movement of k pollutants In coastal urban region a numerical simulation shouts be consider atmospheric flow field with land-sea breeze, mountain-valley wand and urban effects. In this study we used Lagrangian [article dispersion method In the atmospheric flow field of Pusan coastal region to depict diffusion and movement of the Pollutants emoted from particular sources and employed two grid system, one for large scale calculating region with the coarse mesh grid (CMG) and the other for the small region with the One mesh 914 (FMG). It was found that the dispersion pattern of the pollutants followed local circulation system in coastal urban area and wale air pollutants exhausted from Sasang moved Into Baekyang and Jang moutain, air pollutants from Janglim moved into Hwameong-dong region.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.1-15
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• 2002

Advection-dominated transport problems possess difficulties in the design of numerical methods for solving them. Because of the hyperbolic nature of advective transport, many characteristic numerical methods have been developed such as the classical characteristic method, the Eulerian-Lagrangian method, the transport diffusion method, the modified method of characteristics, the operator splitting method, the Eulerian-Lagrangian localized adjoint method, the characteristic mixed method, and the Eulerian-Lagrangian mixed discontinuous method. In this paper relationships among these characteristic methods are examined. In particular, we show that these sometimes diverse methods can be given a unified formulation. This paper focuses on characteristic finite element methods. Similar examination can be presented for characteristic finite difference methods.

• 한국연소학회지
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• 제6권2호
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• pp.23-28
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• 2001

In the present work, the effect of PDF selection and intermittency on the result of the numerical simulation are examined by the simulation of a turbulent methane-air jet diffusion flame. As to the PDFs, beta-function and clipped Gaussian are considered. Results for the pure mixing jet are compared with experimental results. Then, the turbulent flame is calculated for the same conditions and the results obtained for the several models are compared. It is found that the clipped Gaussian distribution coupled with consideration of intermittency recovers the experimental data very well. As to the reacting flow results, the main overall properties of the turbulent jet diffusion flame such as maximum flame temperature are less affected by the choice of the PDF. Flame height and NO emissions, on the contrary, appear to be significantly influenced.

• Computers and Concrete
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• 제4권4호
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• pp.273-284
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• 2007

The paper considers a theoretical model for the study of the process of transfer of sulfate ions in saturated porous media - mineral composites. In its turn, the model treats diffusion of sulfate ions into cement based composites, accounting for simultaneous effects such as filling of micro-capillaries with ions and chemical products and liquid push out of them. The proposed numerical algorithm enables one to account for those simultaneous effects, as well as to model the diffusive behavior of separate sections of the considered volume, such as inert fillers. The cases studied illustrate the capabilities of the proposed model and those of the algorithm developed to study diffusion, considering the specimen complex configuration. Computations show that the theoretical assumptions enable one to qualitatively estimate the experimental evidence and the capabilities of the studied composite. The results found can be used to both assess the sulfate corrosion in saturated systems and predict and estimate damage of structures built of cement-based mineral composites.

• 한국대기환경학회지
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• 제12권1호
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• pp.29-41
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• 1996

The two-stage numerical model was used to study the relation between three-dimensional local wind model, advection/diffusion model of random walk method and second moment method on Pusan coastal area. The first stage is three dimensional time-dependent local wind model which gives the wind field and vertical dirrusion coefficient. The second stage is advection/diffusion model which uses the results of the first stage as input data. First, wind fields on Pusan coastal area for none synoptic scale wind showed typical land and sea breeze circulation, and convergence zone occured at 1200LST in northern of domain, in succession, moved northward of domain. Emissions from Sinpyeong industrial district were trasnported toward the inland by sea breeze during daytime, and reached the end part of domain about 1800LST. During nighttime, emissions return to sea by land breeze and vertical diffusion also contributes to upward transport. In order to use this model for forecast of air pollution concentration on the Pusan coastal area, it is necessary that computed value must be compared with measured value and wind fields model must also be dealt in detail.