• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.381-394
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• 2011

In this paper, a Naveir-Stokes equation is solved by using the Adomian's decomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 춘계학술대회논문집
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• pp.13-16
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• 2008

After the collapse of the Tacoma bay bridge at Tacoma Washington, the accurate prediction of aerodynamics became crucial to the sound design of bridges. CFD(Computational Fluid Dynamics) becomes important tool for the prediction on wind effects on the bridge due to the recent development of CFD. The usage of CFD is further prompted by the advantages in using CFD, such as low-cost and fast feed-back of design. In this paper, an unsteady compressible Reynolds averaged Navier-Stokes code is used for the computation of the flow over bridges. Coakley's ��q-${\omega}$ �� two-equation turbulence model is used for the turbulent eddy viscosity. For accurate and stable computations, the local preconditioning method is adapted to the code. Aerodynamic characteristics of a couple bridges are presented to show the validity and the accuracy of the method.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.307-321
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• 2004

In this paper, the unsteady Stokes problem is considered and also the pressure-correction method for the problem is described. At a fixed time level, we reduce the problem to two symmetric positive definite problems which depend on a time step parameter. Linear systems that arise from the problems are large, sparse, symmetric, positive definite and ill-conditioned as the time step tends to zero. Preconditioned problems based on an additive Schwarz method for solving the symmetric positive definite problems are derived and preconditioners are defined implicitly. It will be shown that the rate of convergence is independent of the mesh parameters as well as the time step size.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제21권3호
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• pp.109-124
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• 2017

The numerical solution of the Stokes equation with discontinuous viscosity and singular force term is challenging, due to the discontinuity of pressure, non-smoothness of velocity, and coupled discontinuities along interface.In this paper, we give an efficient algorithm to solve this problem by employing spectral Legendre and Chebyshev approximations.First, we present the algorithm for a problem defined in rectangular domain with straight line interface. Then it is generalized to a domain with smooth curve boundary and interface by employing spectral element method. Numerical experiments demonstrate the accuracy and efficiency of our algorithm and its spectral convergence.

• 대한기계학회논문집B
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• 제20권3호
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• pp.1015-1027
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• 1996

In this paper, a numerical procedure for the calculation of the incompressible Navier-Stokes equations in a generalized nonorthogonal body fitted coordinate system is proposed and is validated through three test problems. Present numerical procedure derives the pressure equation by using the pressure substitution method on the regular grid system, and discretized momentum equations are based on the covariant velocity components. Cavity flow, backward facing step flow, and two dimensional channel flow with a sinusoidal wavy wall are chosen as three test problems. Numerical solutions obtained by present procedure shows a good agreement with previous numerical and/or experimental results. Convergence rate is also satisfactory.

• 대한화학회지
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• 제44권4호
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• pp.350-355
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• 2000

알루미늄 보레이트 화합물, $CaAl_2(BO_3)_2O$와 $BaAl_2(BO_3)_2O$은 매우 효과적으로 $Eu^{2+}$ 이온의 형광성을 나타내는 발광격자를 가지고 있다. 발광피크는 $Eu^{2+}$:$CaAl_2(BO_3)_2O$화합물에 있어서 450㎚이고 $Eu^{2+}$:$SrAl_2(BO_3)_2O$화합물에 있어서411㎚이며 $Eu^{2+}$:$BaAl_2(BO_3)_2O$ 화합물에 있어서 375㎚이다. 그러므로 $Eu^{2+}$:$CaAl_2(BO_3)_2O$ 화합물은 파란색을 내는 좋은 형광체이며, 특별히, 진공자외선 제논 플라마스 램프에 있어서 우수한 형광물질로 기대된다. $Eu^{2+}$ 이온은 PDP 형광체로써 관심이 높으며, Stokes shift는 형광물질의 도핑격자 크기에 의해서 결정이 된다. Stokes shift는 발광 파장을 결정하는 하나의 중요한 요소이다. 만일, 도핑격자의 크기가작아짐에 따라 $Eu^{2+}$ 이온의 5d 에너지 준위가 낮아지면, 발광 파장은 길어지고 Stokes shift크기는 커진다. 그러므로 결정격자의 크기를 측정하면 $Eu^{2+}$ 이온의 Stokes shift와 5d 에너지 준위 등의 발광성질을 예측할 수 있다.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.383-405
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• 2004

We study the incomprssible Navier Stokes equations for the flow inside contraction geometry. The governing equations are expressed in the vorticity-stream function formulations. A rectangular computational domain is arised by elliptic grid generation technique. The numerical solution is based on a technique of automatic numerical generation of acurvilinear coordinate system by transforming the governing equation into computational plane. The transformed equations are approximated using central differences and solved simultaneously by successive over relaxation iteration. The time dependent of the vorticity equation solved by using explicit marching procedure. We will apply the technique on several irregular-shapes.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권3호
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• pp.155-162
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• 2018

We describe a parallel implementation of a relaxed Hermitian and skew-Hermitian splitting preconditioner for the numerical solution of saddle point problems arising from the steady incompressible Navier-Stokes equations. The equations are linearized by the Picard iteration and discretized with the finite element and finite difference schemes on two-dimensional and three-dimensional domains. We report strong scalability results for up to 32 cores.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2002년도 추계학술대회 논문집
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• pp.212-216
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• 2002

평행한 벽 내부의 흐르는 규제 속에 원형실린더를 놓고 운동장 해석을 수행하였다. 비압축성 Navier- Stokes 방정식을 풀었고 3차 풍상미분의 수치해법을 이용하였다. 채널 내부에서 실린더의 위치를 이동하면서 벽면의 효과 전단력, 와류의 현장을 규명하였다. 수치처리는 Marker & Cell 기법에 의한 유한차분법을 사용하였다. 본 연구를 통하여 실린더와 벽 경계 사이에서의 생성된 와가 박리 전단에 영향을 미치는 것을 알 수 있었다.

• 한국해양공학회지
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• 제1권1호
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• pp.65-72
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• 1987

두개의 동일한 원통이 두중심점을 잇는 선에 대하여 수직인 방향으로 저동할때 발생되는 정상류에 대한 해를 구하였다. 관련된 자변수들간의 어떤 가정하에서 본문제는 Stokes문제가 될 수 있었다. 유동함수를 급수전개하였으며, 급수의 계수수함수는 penta-diagonal matrix를 풀어 구할 수 있었다. 해의 결과에 의하면 원통 주위에 몇개의 소용돌이가 생겼며 그소용돌이의 수는 두 원통간의 거리에 따라 달라 졌다. 두 원통간의 거리가 커짐에 따른 점근적 성질을 단일 원통의 경우와 비교하여 확인하였다.