• 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.

• 대한기계학회논문집B
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• 제27권9호
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• pp.1327-1334
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• 2003

Flow characteristics of the fluid laden with many particles in the two-dimensional channel are investigated using the Navier-Stokes equations coupled with the equation of motion of particles by direct numerical simulation. A four-step fractional step method with Crank-Nicolson scheme and ALE technique is used for P2P1 mixed finite element method. The motion and distribution of particles in the fluid is virtually described as a result of direct numerical simulation and the increase of viscosity is compared with theoretical equations. The effect of channel height on the relative viscosity and the tubular pinch effect are discussed.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.910-915
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• 2003

A Navier-Stokes equation solver for incompressible viscous flows with free surface is developed and tested. This is based upon a fractional time step method and a non-staggered finite volume formulation for unstructured meshes. For time advancement scheme, Adams -Bashforth method for convective term and Crank-Nicolson method for diffusive term are applied. The interface between two fluids with different fluid properties is tracked with Piecewise Linear Interface Calculation(PLIC) Volume-of-Fluid(VOF) methods. Computational results are presented for some test problems: the broken dam, the sloshing in a rectangular tank, the filling of a cylindrical tank.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권2호
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• pp.123-135
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• 2015

In this paper, a reduced-order modeling(ROM) of Burgers equations is studied based on pseudo-spectral collocation method. A ROM basis is obtained by the proper orthogonal decomposition(POD). Crank-Nicolson scheme is applied in time discretization and the pseudo-spectral element collocation method is adopted to solve linearlized equation based on the Newton method in spatial discretization. We deliver POD-based algorithm and present some numerical experiments to show the efficiency of our proposed method.

• 한국항만학회지
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• 제12권2호
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• pp.281-290
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• 1998

The propagation of water waves over irregular bottom bathymetry and around islands involves many process-shoaling, refraction, energy dissipation and diffraction. Numerical model in this study is developed with the mild slope equation to investigate wave transformation in water of varying depth and combined waves and a current. The method used is splitting method and minimax approximation. The numerical method used in this study is Crank-Nicolson scheme in the FDM. This model is applied to Vincent shoal and compared with laboratory experimental data. The results agreed well with laboratory data. Current effect is considered in this study. This model can be used for the estimation of rip current in the slowly varying topography.

• Journal of the Optical Society of Korea
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• 제12권2호
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• pp.112-117
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• 2008

Single-mode propagation conditions of X-ray waveguides are investigated by numerical calculations in order to understand the importance of waveguide design parameters, such as core thickness and the optical constants of waveguide materials, on the transmission and coherence properties of the waveguide. The simulation code for mode analyzing is developed based on a numerical solution of the parabolic wave equation. The initial boundary value problem is solved numerically using a finite-difference scheme based on the Crank-Nicolson scheme. The E-field intensities in a core layer are calculated at an X-ray energy of 8.0 keV for air and beryllium(Be) core waveguides with different cladding layers such as Pt, Au, W, Ni and Si to determine the dependence on waveguide materials. The highest E-field intensity radiated at the exit of the waveguide is obtained from the Pt cladded beryllium core with a thickness of 20 nm. However, the intensity from the air core waveguide with Pt cladding reaches 64% of the Be-Pt waveguide. The dependence on the core thickness, which is the major parameter used to generate a single mode in the waveguide, is investigated for the air-Pt, and Be-Pt waveguides at an X-ray energy of 8.0 keV. The mode profiles at the exit are shown for the single mode at a thickness of up to 20 nm for the air-Pt and the Be-Pt waveguides.

• 대한토목학회논문집
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• 제14권3호
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• pp.619-633
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• 1994

천해역(淺海域)에서 굴절(屈折), 회절(回折) 및 쇄파(碎波)를 고려한 범용성(汎用性)있는 파랑변형모형(波浪變形模型)을 개발하였다. 기존(旣存)이 완경사방정식(緩傾斜方程式)으로부터 고차(高次)의 회절항(回折項)을 고려한 포물형근사방정식(抛物形近似方程式)을 유도하였으며, 난류모형(亂流模型)을 도입하여 저면마찰(底面摩擦) 및 쇄파(碎波)에 의한 에너지 감쇠항(減衰項)을 정식화(定式化)하였다. 본 모형(模型)의 수치해(數値解)는 Crank-Nicolson의 음해법(陰解法)으로 계산하였으며, 계산결과(計算結果)는 원형천퇴(圓形淺堆), 타원형천퇴(楕圓形淺堆) 및 쇄파대(碎波帶)에서의 여러가지 수리실험결과(水理實驗結果)와 비교하였다. 쇄파대(碎波帶)에서 파고감쇠양상(波高減衰樣相)은 입사파(入射波)의 파형경사(波形傾斜)에 따라 민감(敏感)하게 반응(反應)하였으며, 타원형천퇴(楕圓形淺堆) 주변(周邊)에서 비선형분산관계(非線型分散關係)와 에너지 감쇠효과(減衰效果)는 파고변화(波高變化)를 잘 설명하였다. 그리고 본 모형(模型)을 현지해안(現地海岸)에 적용하여 타당성(妥當性)있는 계산결과(計算結果)를 얻었다.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2005년도 학술발표회 논문집
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• pp.414-418
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• 2005

A finite element model is developed for the numerical simulation of bed elevation change in a curved channel. The SU/PG (Streamline-Upwind/Petrov-Galerkin) method is used to solve 2D shallow water equations and the BG (Bubnov-Galerkin) method is used for the Exner equation. For the time derivative terms, the Crank-Nicolson scheme is used. The developed model is a decoupled model in a sense that the bed elevation does not change simultaneously with the flow during the computational time step. The total load formula with is used for the sediment transport model. The slip conditions are described along the lateral boundaries. The effects of gravity force due to geometry change and the secondary flows in a curved channel are considered in the model. For the verification, the model is applied to two laboratory experiments. The first is $140^{\circ}$ bended channel data at Delft Hydraulics Laboratory and the second is $140^{\circ}$ bended channel data at Laboratory of Fluid Mechanics of the Delft University of Technology. The finite element grid is constructed with linear quadrilateral elements. It is found that the computed results are in good agreement with measured data, showing a point bar at the inner bank and a pool at the outer bank.

• Korea-Australia Rheology Journal
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• 제21권1호
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• pp.47-58
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• 2009

We have investigated the transient behavior of 1D fully developed Poiseuille viscoelastic flow under finite pressure gradient described by the Oldroyd-B and Leonov constitutive equations. For analysis we employ a simple $2^{nd}$ order discretization scheme such as central difference for space and the Crank-Nicolson for time approximation. For the analysis of the Oldroyd-B model, we also apply the analytical solution, which is obtained again in this work in terms of elementary solution procedure simpler than the previous one (Waters and King, 1970). Both models demonstrate qualitatively similar solutions, but their eventual steady flowrate exhibits noticeable difference due to the absence or presence of shear thinning behavior. In the inertialess flow, the flowrate instantaneously attains a large value corresponding to the Newtonian creeping flow and then decreases to its steady value when the applied pressure gradient is low. However with finite liquid density the flow field shows severe fluctuation even accompanying reversals of flow directions. As the assigned pressure gradient increases, the flowrate achieves its steady value significantly higher than its value during oscillations after quite long period of time. We have also illustrated comparison between 1D and 2D results and possible mechanism of complex 2D flow rearrangement employing a previous solution of [mite element computation. In addition, we discuss some mathematical points regarding missing boundary conditions in 2D modeling due to the change of the type of differential equations when varying from inertialess to inertial flow.

• 한국재료학회지
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• 제29권9호
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• pp.547-552
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• 2019

In the present study, the thermal conductivity of a silicon nitride($Si_3N_4$) thin-film is evaluated using the dual-wavelength pump-probe technique. A 100-nm thick $Si_3N_4$ film is deposited on a silicon (100) wafer using the radio frequency plasma enhanced chemical vapor deposition technique and film structural characteristics are observed using the X-ray reflectivity technique. The film's thermal conductivity is measured using a pump-probe setup powered by a femtosecond laser system of which pump-beam wavelength is frequency-doubled using a beta barium borate crystal. A multilayer transient heat conduction equation is numerically solved to quantify the film property. A finite difference method based on the Crank-Nicolson scheme is employed for the computation so that the experimental data can be curve-fitted. Results show that the thermal conductivity value of the film is lower than that of its bulk status by an order of magnitude. This investigation offers an effective way to evaluate thermophysical properties of nanoscale ceramic and dielectric materials with high temporal and spatial resolutions.