• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.699-713
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• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.

• Journal of the Mineralogical Society of Korea
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• v.25 no.4
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• pp.211-220
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• 2012

The numerical modeling and simulation have been used increasingly as tools for examining and interpreting the bulk structure and properties of materials. The use of molecular dynamics (MD) simulations to model the structure of materials is now both widespread and reasonably well understood. In this research, we introduced the numerical method to calculate the physico-chemical properties such as a diffusion coefficient and a viscosity of clay mineral. In this research, a series of MD calculations were performed for clay mineral and clay-water systems, appropriate to a saturated deep geological setting. Then, by using homogenization analysis (HA), the diffusion coefficients are calculated for conditions of the spatial distribution of the water viscosity associated with some configuration of clay minerals. This result of numerical analysis is quite similar to the previous experimental results. It means that the introduced numerical method is very useful to calculate the physico-chemical properties of clay minerals under various environmental conditions.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.231-249
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• 2020

We present an efficient and robust finite difference method for a two-asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.33 no.4
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• pp.288-297
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• 2009

A serpentine channel geometry often used in a fuel cell has a strong pressure gradient between adjacent channels in specific regions. The pressure gradient helps some amount of reactant gas penetrate through a gas diffusion layer(GDL). As a result, the overall serpentine flow structure is slightly different from the intention of a designer. The purpose of this paper is to examine the effect of serpentine flow structure on current density distribution. By using a commercial code, STAR-CD, a numerical simulation is performed to analyze the fuel cell with high aspect ratio of active area. To increase the accuracy of the numerical simulation, GDL permeabilities are measured with various compressive forces. Three-dimensional flow field and current density distribution are calculated. For the verification of the numerical simulation results, water condensation process in the cathode channel is observed through a transparent bipolar plate. The result of this study shows that the region of relatively low current density corresponds that of dropwise condensation in cathode channels.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.27-41
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• 2014

In this paper, we present an efficient numerical method for multiphase image segmentation using a multiphase-field model. The method combines the vector-valued Allen-Cahn phase-field equation with initial data fitting terms containing prescribed interface width and fidelity constants. An efficient numerical solution is achieved using the recently developed hybrid operator splitting method for the vector-valued Allen-Cahn phase-field equation. We split the modified vector-valued Allen-Cahn equation into a nonlinear equation and a linear diffusion equation with a source term. The linear diffusion equation is discretized using an implicit scheme and the resulting implicit discrete system of equations is solved by a multigrid method. The nonlinear equation is solved semi-analytically using a closed-form solution. And by treating the source term of the linear diffusion equation explicitly, we solve the modified vector-valued Allen-Cahn equation in a decoupled way. By decoupling the governing equation, we can speed up the segmentation process with multiple phases. We perform some characteristic numerical experiments for multiphase image segmentation.

• 한국신재생에너지학회:학술대회논문집
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• 2007.11a
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• pp.147-151
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• 2007

A serpentine channel geometry often used in a polymer electrolyte membrane fuel cell has a strong pressure gradient between adjacent channels in specific regions. The pressure gradient helps some amount of reactant gas penetrate through a gas diffusion layer(GDL). As a result, the overall serpentine flow structure is slightly different from intention of a designer. The purpose of this paper is to examine the effect of serpentine flow structure on current density distribution. By using a commercial code, STAR-CD, a numerical simulation is performed to analyze the fuel cell with relatively high aspect ratio active area. To increase the accuracy of the numerical simulation, GDL permeabilities are measured with various compression conditions. Three-dimensional flow field and current density distribution are calculated. For the verification of the numerical simulation results, water condensation process in the cathode channel is observed through a transparent bipolar plate. The result of this study shows that the region of relatively low current density corresponds to that of dropwise condensation in cathode channels.

• Journal of Environmental Science International
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• v.2 no.1
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• pp.17-26
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• 1993

The layer that is directly influenced by ground surface is called the atmospheric boutsdary layer in comparison with the free atmosphere of higher layer. In the boundary layer, the changes of wind, temperature and coefficient of turbulent diffusion in altitude are large and have great influences an atmospheric diffusion. The purpose of this paper is to express the structure and characteristics of development of mixed layer by using laboratory experiment and numerical simulation. Laboratory experiment using water tank are performed that closely simulate the process of break up of nocturnal surface inversion above heated surface and its phenomena are analyzed by the use of horizontally averaged temperature which is observed. The result obtained from the laboratory experiment is compared with theoretical ones from ; \textsc{k}-\varepsilon numerical model. The results are summarized as follows. 1) The horizontally averaged temperature was found to vary smoothly with height and the mixed layer developed obviously being affected by the convection. 2) The mean height of mixed layer may be predicted as a function of time, knowing the mean initial temperature gradient. The experimental values are associated well with the theoretical values computed for value of the universal constant $C_r$= 0.16, our $C_r$ value is little smaller than the value found by Townsend and Deardoru et al.

• Computers and Concrete
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• v.23 no.1
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• pp.69-80
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• 2019

Modeling approach for mesoscopic model of concrete depicting mass transportation and physicochemical reaction is important since there is growing demand for accuracy and computational efficiency of numerical simulation. Mesoscopic numerical simulation considering binder, aggregate and Interfacial Transition Zone (ITZ) generally produces huge number of DOFs, which is inapplicable for full structure. In this paper, a three-dimensional multiscale approach describing three-phase structure of concrete was discussed numerically. An effective approach generating random aggregate in polygon based on checking centroid distance was introduced. Moreover, ITZ elements were built by parallel expanding the surface of aggregates on inner side. By combining mesoscopic model including full-graded aggregate and macroscopic model, cases related to diffusivity and thickness of ITZ, volume fraction and grade of aggregate were studied regarding the consideration of multiscale compensation. Results clearly showed that larger analysis model in multiscale model expanded the diffusion space of chloride ion and decreased chloride content in front of rebar. Finally, this paper addressed some worth-noting conclusions about the chloride distribution and rebar corrosion regarding the configuration of, rebar diameter, concrete cover and exposure period.

• Journal of the Korea Safety Management & Science
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• v.20 no.4
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• pp.7-13
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• 2018

This study investigates the enhancement of the oxygen diffusion rate in the cathode channel of a proton exchange membrane fuel cell (PEMFC) by pure oscillating flow, which is the same as the mechanism of human breathe. Three-dimensional numerical simulation, which has the full model of the fuel cell including electrochemical reaction, ion and electronic conduction, mass transfer and thermal variation and so on, is performed to show the phenomena in the channel at the case of a steady state. This model could analysis the oscillating flow as a moving mesh calculation coupled with electrochemical reaction on the catalyst layer, however, it needs a lot of calculation time for each case. The two dimensional numerical simulation has carried on for the study of oscillating flow effect in the cathode channel of PEMFC in order to reduce the calculation time. This study shows the diffusion rate of the oxygen increased and the emission rate of the water vapor increased in the channel by oscillating flow without any forced flow.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.249-281
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• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.