• 대한기계학회논문집B
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• 제24권10호
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• pp.1317-1325
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• 2000

A new efficient numerical method for computing three-dimensional, unsteady, incompressible flows is presented. To eliminate the restriction of CFL condition, a fully-implicit time advancement in which the Crank-Nicolson method is used for both the diffusion and convection terms, is adopted. Based on an approximate block LU decomposition method, the velocity -pressure decoupling is achieved. The additional decoupling of the intermediate velocity components in the convection term is made for the fully -implicit time advancement scheme. Since the iterative procedures for the momentum equations are not required, the velocity components decouplings bring forth the reduction of computational cost. The second-order accuracy in time of the present numerical algorithm is ascertained by computing decaying vortices. The present decoupling method is applied to minimal channel flow unit with DNS (Direct Numerical Simulation).

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집B
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• pp.704-708
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• 2000

A new efficient numerical method for computing unsteady, incompressible flows, DRANS (Decoupled Reynolds-Averaged Navier-Stokes), is presented. To eliminate the restriction of CFL condition, a fully-implicit time advancement in which the Crank-Nicolson method is used fer both the diffusion and convection terms. is adopted. Based on decomposition method, the velocity-turbulent quantity decoupling is achieved. The additional decoupling of the intermediate velocity components in the convection term is made for the fully-implicit time advancement scheme. Since the iterative procedures for the momentum, ${\kappa}\;and\;{\varepsilon}$ equations are not required, the components decouplings bring fourth the reduction of computational cost. The second-order accuracy in time of the present numerical algorithm is ascertained by computing decaying vortices. The present decoupling method is applied to turbulent boundary layer with local forcing.

• 대한수학회논문집
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• 제14권4호
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• pp.833-842
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• 1999

In this paper, we construct a fully discrete solution of the incompressible Navier Stokes equations using implicit Runge kutta method. We prove the existence of the fully discrete solution.

• Nuclear Engineering and Technology
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• 제41권7호
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• pp.885-892
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• 2009

This manuscript will discuss a numerical method where the six equations of two-phase flow, the solid heat conduction equations, and the two equations that describe neutron diffusion and precursor concentration are solved together in a tightly coupled, nonlinear fashion for a simplified model of a nuclear reactor core. This approach has two important advantages. The first advantage is a higher level of accuracy. Because the equations are solved together in a single nonlinear system, the solution is more accurate than the traditional "operator split" approach where the two-phase flow equations are solved first, the heat conduction is solved second and the neutron diffusion is solved third, limiting the temporal accuracy to $1^{st}$ order because the nonlinear coupling between the physics is handled explicitly. The second advantage of the method described in this manuscript is that the time step control in the fully implicit system can be based on the timescale of the solution rather than a stability-based time step restriction like the material Courant limit required of operator-split methods. In this work, a pilot code was used which employs this tightly coupled, fully implicit method to simulate a reactor core. Results are presented from a simulated control rod movement which show $2^{nd}$ order accuracy in time. Also described in this paper is a simulated rod ejection demonstrating how the fastest timescale of the problem can change between the state variables of neutronics, conduction and two-phase flow during the course of a transient.

• 한국항공우주학회지
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• 제38권12호
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• pp.1153-1161
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• 2010

본 연구에서는 주기적 비정상 유동 해석을 위해 푸리에 변환을 이용하는 조화 균형법의 효율적인 해법을 제안한다. 내재적으로 유속항을 처리하고 외재적으로 조화 원천항을 처리하였다. 외재적 조화 균형법 보다 더 빠르게 수렴 시킬 수 있으며 내재적 조화 균형법을 적용할 때 추가되는 자코비안 행렬을 처리할 필요가 없다. 또한 완전 내재적 기법에 상응하는 수준의 수렴안정성을 확인할 수 있었다. 2차원 비정상 유동 문제로 피칭하는 NACA0012 익형에 적용하였으며 이중 시간 적분법 및 외재적 Runge-Kutta기법의 해와 매우 일치하는 결과를 얻었다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회A
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• pp.512-517
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• 2007

In the previous development of the recursive thermostat chained fully flexible cell molecular dynamics simulation, implicit time integration method such as generalized leapfrog integration is used. The implicit algorithm is very much complicated and not easy to show time reversibility because it is solved by the nonlinear iterative procedure. Thus we develop simple, explicit symplectic time integration formula for the recursive thermostat chained fully flexible unit cell simulation. Uniaxial tension test is performed to verify the present explicit algorithm. We check that the present simulation satisfies the ergodic hypothesis for various values of fictitious mass and coefficient of multiple thermostat system. The proposed method should be helpful to predict mechanical and thermal behavior of nano-scale structure.

• 대한수학회보
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• 제48권2호
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• pp.413-426
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• 2011

Two types of new methods with variable time steps are proposed in order to valuate binary options efficiently. Type I changes adaptively the size of the time step at each time based on the magnitude of the local error, while Type II combines two uniform meshes. The new methods are hybrid finite difference methods, namely starting the computation with a fully implicit finite difference method for a few time steps for accuracy then performing a ${\theta}$-method during the rest of computation for efficiency. Numerical experiments for standard European vanilla, binary and American options show that both Type I and II variable time step methods are much more efficient than the fully implicit method or hybrid methods with uniform time steps.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• 대한토목학회논문집
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• 제13권3호
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• pp.119-127
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• 1993

근래 천수방정식과 같은 2차원 수치해석에서 가장 널리 쓰이는 방법 중의 하나로 ADI 방법을 들 수 있다. 그러나 서해안과 같이 수심의 변화가 심하며 특히 해저협곡이 곳곳에 발달된 해역에서 조석에 관한 문제해결시 ADI 방법을 사용하면 소위 ADI 효과가 크게 우려된다. 이를 극복하기 위하여 완전 음해법으로 차분되고 CGS(conjugate gradient squared) 방법으로 해를 구하는 알고리즘을 개발하였다. 조간대 모의가 포함된 본 모형용 새만금 수역에 적용한 결과 지형의 복잡성에도 불구하고 유속장과 조간대 형성에 관한 수치적 모의가 만족스러운 결과를 보였다.

• 한국수산과학회지
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• 제18권1호
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• pp.15-22
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• 1985

The study on computation time, accuracy, and convergency characteristic of the implicit finite difference method is presented with the variation of the space increment and time step in a two-dimensional transient heat conduction problem with a dirichlet boundary condition. Numerical analysis were conducted by the model having the conditions of the solution domain from 0 to 3m, thermal diffusivity of 1.26 $m^2/h$, initial condition of 272 K, and boundary condition of 255.4 K. The results obtained are summarized as follows : 1) The degree of influence with respect to the accuracy of the time step and space increment in the alternating-direction implicit method and Crank-Nicholson implicit method were relatively small, but in case of the fully implicit method showed opposite tendency. 2) To prescribe near the zero for the space increment and tine step in a two dimensional transient problem were good in a accuracy aspect but unreasonable in a computational time aspect. 3) The reasonable condition of the space increment and the time step considering accuracy and computation time could be generalized with the Fourier modulus increment, F, ana dimensionless space increment, X, irrespective of the solution domain.