• Proceedings of the Korean Nuclear Society Conference
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• 2004.10a
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• pp.151-152
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• 2004

An acceleration technique combined with the discrete ordinates method which has been widely used in the solution of neutron transport phenomena is applied to the solution of radiative transfer equation. The self-adjoint form of the second order radiation intensity equation is used to enhance the stability of the solution, and a new linearization method is developed to avoid the nonlinearity of the material temperature equation. This new acceleration method is applied to the well known Marshak wave problem, and the numerical result is compared with that of a non-accelerated calculation

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.411-423
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• 2008

In the field of population dynamics and chemical reaction the possibility or the existence of spatially and temporally nonhomogeneous solutions is a very important problem. For last 50 years or so there have been many results on the pattern formation of chemical reaction systems studying reaction systems with or without diffusions to explain instabilities and nonhomogeneous states arising in biological situations. In this paper we study time-dependent properties of a predator-prey system with functional response and give sufficient conditions that guarantee the existence of stable limit cycles.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.6
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• pp.726-733
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• 2004

The growth of the critical size bubble by diffusion process in viscoelastic medium was treated by an integral method for the concentration boundary layer adjacent to the bubble wall. In this study, we obtained a set of the first order time dependent equations to obtain bubble radius and gas pressure inside the bubble simultaneously. The calculated final cell sizes depending on the initial saturation pressure are in close agreement with the observed ones. The governing equations developed in this study may be used in polymer processing of microcellular foams.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• Journal of Environmental Science International
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• v.7 no.4
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• pp.511-522
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• 1998

The two-stage numerical model was used to study the relation between three-dimensional local wind seal area for Korean peninsula. The first stave is three dimensional time-dependent local wind model which elves the wind field and vertical diffusion coefncient. The second stage is advection/duusion model which uses the results of the first stage as input data. First, wand fields on Korean peninsula for none synoptic scale wand showed typical land and sea breeze circulation, and the emitted particles were transported by sea breeze for daytime, emissions return to sea by land breeze for nighttime.

• 한국연소학회:학술대회논문집
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• 2000.12a
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• pp.113-122
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• 2000

Dynamic structures of unsteady $CH_4$/Air jet diffusion flames with flame-vortex interaction were numerically investigated. A time-dependent, axisymmetric computational model was adopted for this calculation. Two step global reaction mechanism which considers 6 species, was used to calculate the reaction rates. The predicted results including gravitational effect show that the large outer vortices and the small inner vortex street can be well simulated without any additional disturbances in the downstream of nozzle tip. It was found that the temperature and species concentrations had various values for the same mixture fraction in flame-vortex interaction region. This unsteady jet flame configuration accompanying flame-vortex interaction is expected to give good implications for the structure of turbulent flames.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.05b
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• pp.189-192
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• 2005

In recent years, many research works have been carried out in order to obtain a more controlled durability and long-term performance of concrete structures in chloride containing environments. In particular, the development of new procedures for probability-based durability analysis/design has proved to be very valuable. In this paper, the equation used for modelling of the chloride penetration was based on Fick's Second Law of Diffusion in combination with a time dependent diffusion coefficient. The probability analysis of the durability performance was performed by use of a Monte Carlo Simulation. The procedure was applied to an example based on limited data gathered in this country. The influences of each parameter on the durability of concrete structures are studied and some comments for durability design are given. The new procedure may be very useful in designing concrete structures in chloride containing environments.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.174-179
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• 2004

The growth of the critical size bubble by diffusion process in viscoelastic medium was treated by an integral method for the concentration boundary layer adjacent to the bubble wall. In this study, we obtained a set of the first order time dependent equations to obtain bubble radius and gas pressure inside the bubble simultaneously. The calculated final cell sizes depending on the initial saturation pressure are in close agreement with the observed ones. The governing equations developed in this study may be used in polymer processing of microcellular foams.

• Membrane Journal
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• v.12 no.2
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• pp.90-96
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• 2002

A novel methodology on the calculations of osmotic pressure and gradient diffusion coefficient has been provided ill the present study, by applying a succinct numerical analysis on the experimental results. Although both the osmotic pressure and the gradient diffusion coefficient represent a fundamental characteristic in related membrane filtrations such as microfiltration and ultrafiltration, neither theoretical analysis nor experiments can readily determine them. The osmotic pressure of colloidal suspension has been successfully determined from a relationship between the data of the time-dependent permeate flux, their numerical accumulations, and their numerical derivatives. It is obvious that the osmotic pressure is gradually increased, as the particle concentration increases. The thermodynamic coefficient was calculated from the numerical differentiation of the correlation equation of osmotic pressure, and the hydrodynamic coefficient was evaluated from the previously developed relation for an ordered system. Finally, the estimated gradient diffusion coefficient, which entirely depends on the particle concentration, was compared to the previous results obtained from the statistical mechanical simulations.