• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.9
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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.

• Proceedings of the KSME Conference
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• 2003.11a
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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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• v.19 no.2
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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.

• Journal of Korean Port Research
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• v.12 no.2
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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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• v.12 no.2
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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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.3
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• pp.619-633
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• 1994

A wave deformation model for general purpose combined refraction, diffraction, and breaking is developed in the shallow water. A parabolic approximation equation considered a higher order diffraction term is derived from the previous mild slope equation. A wave energy dissipation term due to bottom friction and breaking is introduced from the turbulence model. The Crank-Nicoloson implicit scheme is used in the numerical calculation, then the solutions are compared with the various hydraulic experiment data in the circular, the elliptic shoal, and the surf zone. The wave height decay in the surf zone is sensitively affected by the incident wave steepness, and the wave height variation around the elliptic shoal is well explained by the non-linear dispersion relation and the wave energy dissipation term. The model is also applied to a field coastal area and reasonable results are obtained.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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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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• v.21 no.1
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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.

• Korean Journal of Materials Research
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• v.29 no.9
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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.

• Geomechanics and Engineering
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• v.8 no.4
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• pp.559-594
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• 2015

A nonlinear creep function incorporated into the elastic visco-plastic model may describe the long-term soil deformation more accurately. However, by applying the conventional procedure, there are challenges to determine the model parameters due to limitation of suitable data points. This paper presents a numerical solution to obtain several parameters simultaneously for a nonlinear elastic visco-plastic (EVP) model using the available consolidation data. The finite difference scheme using the Crank-Nicolson procedure is applied to solve a set of coupled partial differential equations of the time dependent strain and pore water pressure dissipation. The model parameters are determined by applying the algorithm of trust-region reflective optimisation in conjunction with the finite difference solution. The proposed method utilises all available consolidation data during dissipation of the excess pore water pressure to determine the required model parameters. Moreover, the reference time in the elastic visco-plastic model can readily be adopted as a unit of time; denoting creep is included in the numerical predictions explicitly from the very first time steps. In this paper, the settlement predictions of thick soft clay layers are presented and discussed to evaluate and compare the accuracy and reliability of the proposed method against the graphical procedure to obtain the model parameters. In addition, comparison of the available experimental results to the numerical predictions confirms the accuracy of the numerical procedure.