• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.603-618
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• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• Journal of Korean Society for Atmospheric Environment
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• v.21 no.5
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• pp.547-555
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• 2005

In this study, an analytical expression for aerosol mass transfer at spherical collector in the low Knudsen number region was obtained. Happel's zero shear stress cell model was extended in the low Knudsen number region and the result was compared with numerical solution results. The zero vorticity model based on the Kuwabara's cell model was also extended in the low Knudsen number region and compared with Happel's results. The results showed that both analytic and numerical solution agree very well with each other in low Knudsen number region. Happel's zero shear stress model also agrees with Kuwabara's zero vorticity model without significant loss of accuracy. The obtained solution converges to the original solution of Lee et al. (1999) when Knudsen number approaches to zero. Subsequently, this study derived most general type of analytic solution for aerosol mass transfer of spherical collector including the finite Knudsen number region.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.458-463
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• 2000

The mechanical structures generally have discontinuous parts such as the cracks, notches and holes owing to various reasons. In this paper, in order to analyze effectively these singularity problems using the finite element method, a mixed analysis method which an analytical solution and finite element solutions are simultaneously used is newly proposed. As the analytical solution is used in the singularity region and the finite element solutions are used in the remaining regions except this singular zone, this analysis method reasonably provides for the numerical solution of a singularity problem. Through various numerical examples, it is shown that the proposed analysis method is very convenient and gives comparatively accurate solution.

• Journal of Soil and Groundwater Environment
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• v.13 no.2
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• pp.54-61
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• 2008

The drawdown distribution due to pumping by horizontal or slanted wells is analyzed by numerical modelling. In the numerical modelling uses 1-D discrete element feature included in commercial groundwater modeling program FEFLOW (version 5.1) and the results are compared with the semi analytic solution which uses superposition of successive point sources proposed by Zhan and Zlotnik (2002). Results of the numerical modeling agree well with the semi analytic solution except for very near field region of sink sources. The drawdown distribution due to pumping in riverbank filtration(RBF) plan site can be evaluated quantitatively by the numerical modeling in this study.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.3
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• pp.27-36
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• 2002

Numerical stability is studied based on numerics and mathematics. It is frequently observed in the region where velocity is zero. In that region, the Euler equation have numerous solutions and, thus, it is impossible to determine a unique solution with only governing equations. However, a unique solution can be determined by additional outer flow conditions or outer numerical discontinuity calculation since the information or a unique solution under undisturbed conditions is lost by disturbances. In this reason, the numerical scheme comsistent with Euler equations cannot remove shock instability completely.

• Journal of Soil and Groundwater Environment
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• v.20 no.2
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• pp.10-21
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• 2015

The present study introduces a novel numerical approach for solving dispersion dominated problems with Cauchy boundary condition in an Eulerian-Lagrangian scheme. The study reveals the incapability of traditional Neuman approach to address the dispersion dominated problems with Cauchy boundary condition, even though it can produce reliable solution in the advection dominated regime. Also, the proposed numerical approach is applied to a real field problem of radioactive contaminant migration from radioactive waste repository which is a major current waste management issue. The performance of the proposed numerical approach is evaluated by comparing the results with numerical solutions of traditional FDM (Finite Difference Method), Neuman approach, and the analytical solution. The results show that the proposed numerical approach yields better and reliable solution for dispersion dominated regime, specifically for Peclet Numbers of less than 0.1. The proposed numerical approach is validated by applying to a real field problem of radioactive contaminant migration from radioactive waste repository of varying Peclet Number from 0.003 to 34.5. The numerical results of Neuman approach overestimates the concentration value with an order of 100 than the proposed approach during the assessment of radioactive contaminant transport from nuclear waste repository. The overestimation of concentration value could be due to the assumption that dispersion is negligible. Also our application problem confirms the existence of real field situation with advection dominated condition and dispersion dominated condition simultaneously as well as the significance or advantage of the proposed approach in the real field problem.

• The Journal of the Korea Contents Association
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• v.13 no.2
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• pp.505-511
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• 2013

A new boundary treatment technique which can be applied to axi-symmetric topography with inclined bottom was developed. Although the finite element method is good for complex geometry, there is no proper boundary treatment when a boundary is not a vertical section because the water depth at the coastline becomes zero. In this study, we developed a new boundary treatment for inclined bottom using the analytical solution for long wave. To develope a model, the mild-slope equation was used and then, a computational domain is divided into an analytical region and a numerical region. By combining a numerical and an analytical solutions, a complete solution was obtained. The developed solution was validated by comparing with a previous analytical solution.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.179-182
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• 2004

This paper deals with a new mathematical formulation of nonlinear wave profile based on Banach fixed point theorem. As application of the formulation and its solution procedure, some numerical solutions was presented in this paper and nonlinear equation was derived. Also we introduce a new operator for iteration and getting solution. A numerical study was accomplished with Stokes' first-order solution and iteration scheme, and then we can know the nonlinear characteristic of Stokes' high-order solution. That is, using only Stokes' first-oder(linear) velocity potential and an initial guess of wave profile, it is possible to realize the corresponding high-oder Stokian wave profile with tile new numerical scheme which is the method of iteration. We proved the mathematical convergence of tile proposed scheme. The nonlinear strategy of iterations has very fast convergence rate, that is, only about 6-10 iterations arc required to obtain a numerically converged solution.

• Journal of Advanced Marine Engineering and Technology
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• v.30 no.4
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• pp.494-504
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• 2006

It is well known that the two-parameter $J-A_2$ solution can well characterize the crack-tip fields and quantify the crack-tip constraint for different flawed geometries in variety of loading conditions. However, this solution fails to do so for bending dominated specimens or geometries at large deformation because of the influence of significant global bending stress on the crack-tip field. To solve this issue, a modified $J-A_2$ solution is developed in this paper by introducing an additional term to address the global bending influence. Using the $J_2$ flow theory of plasticity and within the small-strain framework detailed finite element analyses are carried out for the single edge notched bend (SENB) specimen with a deep crack in A533B steel at different deformation levels ranging from small-scale Yielding to large-scale Yielding conditions. The numerical results of the crack-tip stress field are then compared with those determined from the $J-A_2$ solution and from the modified $J-A_2$ solution at the same level of applied loading Results indicate that the modified $J-A_2$ solution largely improves the $J-A_2$ solution, and match very well with the numerical results in the region of interest at all deformation levels. Therefore, the proposed solution can effectively describe the crack-tip field and the constraint for bending dominated specimens or geometries.

• Journal of the Korean Society of Hazard Mitigation
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• v.11 no.3
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• pp.111-116
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• 2011

Analytical solutions for laterally loaded piles were derived. Critical pile length which can be considered as the length for behaving as long pile was investigated varying with densities of sandy soils. Lateral behaviors obtained from analytical solution and numerical solution were also investigated. Non-dimensional critical pile lengths obtained from analytical solutions for three types of pile head boundary conditions were 2.3~3.2. By comparing analytical solutions with numerical solutions, distribution of pile deflection and that of moment were similar and it can be seen that pile head deflection obtained by analytical method is conservative. And the values of moments were not too different between analytical solution and numerical solution.