• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.169-174
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• 1995

A finite element scheme using the concept of PISO method has been developed to solve the viscous flow problems in all speed range. In this study, new pressure equation is proposed such that both the hyperbolic term related with the density variations and elliptic term reflecting the incompressibility constraint are included. Present method has been applied to incompressible flow in two-dimensional driven cavity(Re=100, 400 and 1,000), and its computed results are compared with other's. Also, Carter plate problem(M=3 and Re=1,000) is computed and the comparison is made with Carter's results. Finally, we simulate a shock-boundary layer interaction problem(M=2 and $Re=2.96{\times}10^5$) to illustrate the shock capturing capability of the present solution algorithm.

• Journal of computational fluids engineering
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• v.5 no.2
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• pp.28-37
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• 2000

An integrated grid generation has been developed for a Navier-Stokes simulation of flow fields inside multistaged turbomachinery The internal grids are generated by the combination of algebraic and elliptic methods. The interactive mode of the present system is coupled efficiently with the design results and flow solvers. Application to several types of axial-flow turbomachines was demonstrated to be reliable and practical as the pre-processor of the computational fluid engineering for gas turbine engines.

• Journal of KSNVE
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• v.3 no.3
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• pp.271-278
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• 1993

Acoustic characteristics of silencer system are affected by various geometric parameters such as cross sectional geometry, size of chamber, and location of inlet-outlet port. It is impossible to obtain exact solutions of the equations of acoustic wave propagation except few simple cases. So, we resort to numerical techniques to analyze performance of acoustic system. In this work, finite element formulation has been obtained to predict transmission loss of an arbitrary 3-dimensional muffler in the presence of mean flow of low mach number. The effect of the degree of the ellipticity of expansion chambers on the transmission loss has been studied using the resulting finite element equation.

• Journal of Ocean Engineering and Technology
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• v.7 no.1
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• pp.156-161
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• 1993

Structures built in the coastal area often cause unexpectedly severe shoreline change on the adjacent beaches. Therefore, beach evolution is one of the most important problem in the coastal engineering. Beach evolution in the coastal area consisted of wave transform model and sediment transport model. Ebersoale's elliptic mild slope equation which considered the effect of combind wave refraction and perline and Dean's one line theory for the sediment transport model were used in this study. Kwangan beach was selected as study area and field observations were done. Numerical simulation for beach evolution in the Kwangan beach was performed and shoreline change predictions were suggested as results.

• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.128-133
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• 2002

The heat transfer characteristics of a turbulent flow in a ribbed two-dimensional channel have been investigated numerically. The fully elliptic governing equations, coupled with a four-equation turbulence model, $\kappa-\omega-\bar{t^2}-\epsilon_t$, are solved by a finite volume method of SIMPLE type. Calculations have been carried out for three rib cross-sections : square, triangular, and semicircular, with various rib pitches and Reynolds numbers. The procedure appears to be satisfactory as the results for the square rib compare favorably with available experimental data and earlier calculation. The optimal rib pitch that yields the maximum heat transfer has been identified. It is also found that the square rib is most effective in enhancing the heat transfer. The semicircular rib, on the other hand, incurs the least amount of pressure drop but the improvement in heat transfer is substantially lower.

• Journal of Industrial Technology
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• v.18
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• pp.61-67
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• 1998

이 논문에서는 Diruchlet 경계 조건을 갖는 비선형 타원형 방정식 $-{\Delta}u+g(u)=f(x)$의 해의 존재에 대한 연구를 하였다. 존재하는 해의 다중성을 증명하기 위하여 임계점 이론과 롤의 정리를 사용하였으며, 대응되는 범함수에 따라서 방정식의 해와 임계점이 동시에 나타난다는 정리를 이용하였다. 이 때 $g(u)=bu^+-au^-$으로 나타날 때 외력항 (방정식의 우변)의 상수로 주어지는 경우 적어도 두 개의 해가 존재한다는 것을 증명하였다. 만약 우변(외력항)의 상수가 음수이거나 0인 경우이 방정식의 해가 존재하지 않거나 자명한 해만 존재하기 때문에 상수는 양수인 것으로 가정하였다.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.10 no.3
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• pp.185-219
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• 1981

To analyze two dimensional incompressible laminar natural convection in a rectangular enclosure heated from below and cooled by a horizontal ceiling and two vertical walls, he primitive Navier-Stokes equations and the energy equation were solved numerically in time dependent form by a marker and cell method. A successive over-relaxation method for the elliptic portion of the problem and an explicit method for the parabolic portion were applied for the range of Grashoff number of $5{\times}10^3\;to\;5{\times}10^4$ to get the transient and steady state dimensionless temperature and velocity profiles. For the range of aspect ratio $L/H{\leqq}2.4$ in which only a pair of convection rolls exists mean Nusselt number calculated are as follows : $$N_{NU}0.89\;N_{Gr}^{0.2}(H/L)^{0.45}$$ By path lines drawn by marker particle trajectories roll number of cellular motion were observed for various aspect ratio of the enclosure.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.41 no.7
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• pp.455-462
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• 2017

The magnetic interaction between elliptic Janus magnetic particles are investigated using a direct simulation method. Each particle is a one-to-one mixture of paramagnetic and nonmagnetic materials. The fluid is assumed to be incompressible Newtonian and nonmagnetic. A uniform magnetic field is applied externally in a horizontal direction. A finite-element-based fictitious domain method is employed to solve the magnetic particulate flow in the creeping flow regime. In the magnetic problem, the magnetic field in the entire domain, including the particles and the fluid, is obtained by solving the governing equation for the magnetic potential. Then, the magnetic forces acting on the particles are calculated via a Maxwell stress tensor formulation. In a single particle problem, it is found that the orientation angle at equilibrium is affected by the aspect ratio of the particle. As for the two-particle interaction, the dynamics and the final conformation of the particles are significantly influenced by the aspect ratio, the orientation, and the spatial positions of the particles. For the given positions of the particles, the fluid flow is also influenced by the orientation of each particle. The self-assembly structure of the particles is not a fixed one, but it varies with the above-mentioned factors.

• Journal of The Korean Society of Agricultural Engineers
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• v.58 no.1
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• pp.81-90
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• 2016

The Agricultural Systems Application Platform (ASAP) provides bottom-up modelling and simulation environment for agricultural engineer. The purpose of this study is to expand usability of the ASAP to the second order partial differential equations: elliptic equations, parabolic equations, and hyperbolic equations. The ASAP is a general-purpose simulation tool which express natural phenomenon with capsulized independent components to simplify implementation and maintenance. To use the ASAP in continuous problems, it is necessary to solve partial differential equations. This study shows usage of the ASAP in elliptic problem, parabolic problem, and hyperbolic problem, and solves of static heat problem, heat transfer problem, and wave problem as examples. The example problems are solved with the ASAP and Finite Difference method (FDM) for verification. The ASAP shows identical results to FDM. These applications are useful to simulate the engineering problem including equilibrium, diffusion and wave problem.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.747-775
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• 2020

In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, $$(P)\;\{(-{\Delta}_p)^su={\lambda}{\mid}u{\mid}^{q-2}u+{\frac{{\mid}u{\mid}^{p{^*_s}(t)-2}u}{{\mid}x{\mid}^t}}{\hspace{10}}in\;{\Omega},\\u=0{\hspace{217}}in\;{\mathbb{R}}^N{\backslash}{\Omega},$$ where Ω ⊂ ℝ^N is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < t < sp < N, 1 < q < p < p^∗_s where $p^*_s={\frac{N_p}{N-sp}}$, $p^*_s(t)={\frac{p(N-t)}{N-sp}}$, are the fractional critical Sobolev and Hardy-Sobolev exponents respectively. The fractional p-laplacian (-∆_p)^su with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by $\displaystyle(-{\Delta}_p)^su(x)=2{\lim_{{\epsilon}{\searrow}0}}\int{_{{\mathbb{R}}^N{\backslash}{B_{\epsilon}}}}\;\frac{{\mid}u(x)-u(y){\mid}^{p-2}(u(x)-u(y))}{{\mid}x-y{\mid}^{N+ps}}dy$, x ∈ ℝ^N. The main goal of this work is to show how the usual variational methods and some analysis techniques can be extended to deal with nonlocal problems involving Sobolev and Hardy nonlinearities. We also prove that for some α ∈ (0, 1), the weak solution to the problem (P) is in C^1,α(${\bar{\Omega}}$).