• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.27-41
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• 2014

In this paper, we present an efficient numerical method for multiphase image segmentation using a multiphase-field model. The method combines the vector-valued Allen-Cahn phase-field equation with initial data fitting terms containing prescribed interface width and fidelity constants. An efficient numerical solution is achieved using the recently developed hybrid operator splitting method for the vector-valued Allen-Cahn phase-field equation. We split the modified vector-valued Allen-Cahn equation into a nonlinear equation and a linear diffusion equation with a source term. The linear diffusion equation is discretized using an implicit scheme and the resulting implicit discrete system of equations is solved by a multigrid method. The nonlinear equation is solved semi-analytically using a closed-form solution. And by treating the source term of the linear diffusion equation explicitly, we solve the modified vector-valued Allen-Cahn equation in a decoupled way. By decoupling the governing equation, we can speed up the segmentation process with multiple phases. We perform some characteristic numerical experiments for multiphase image segmentation.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.519-532
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• 2020

In this paper, we first propose a new total variation-based regularization model for image restoration. We next propose a fixed-point-like method for solving the new image restoration model, and then we provide convergence analysis for the fixed-point-like method. To evaluate the feasibility and efficiency of the fixed-point-like method for the new proposed total variation-based regularization model, we provide numerical experiments for several test problems.

• Journal of computational fluids engineering
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• v.15 no.4
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• pp.99-108
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• 2010

Fractional Step Methods(FSM) are popular in simulation of unsteady incompressible flow. In this study, we demonstrate that FSM, combined with a Volume-Of-Fluid method, can be further applied to simulation of multiphase flow. The interface between the fluids is constructed by the effective least squares volume-of-fluid interface reconstruction algorithm and advected by the velocity using the operator split advection algorithm. To verify our numerical methodology, our results are compared with other authors' numerical and experimental results for the benchmark problems, revealing excellent agreement. The present FSM sheds light on accurate simulation of turbulent multiphase flow which is found in many engineering applications.

• Journal of the Korea Society of Computer and Information
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• v.17 no.7
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• pp.67-76
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• 2012

This paper proposes an efficient method that helps a visually impaired person to detect a pavement borderline. A pedestrian is equipped with a camera so that the front view of a natural scene is captured. Our approach analyzes the captured image and detects the borderline of a pavement in a very robust manner. Our approach performs the task in two steps. In a first step, our approach detects a vanishing point and vanishing lines by applying an edge operator. The edge operator is designed to take a threshold value adaptively so that it can handle a dynamic environment robustly. The second step is to determine the borderlines of a pavement based on vanishing lines detected in the first step. It analyzes the vanishing lines to form VRays that confines the pavement only. The VRays segments out the pavement region in a radial manner. We compared our approach against Canny edge detector. Experimental results show that our approach detects borderlines of a pavement very accurately in various situations.

• Journal of the Korean Society of Combustion
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• v.6 no.2
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• pp.15-22
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• 2001

A pressure-based, unstructured finite volume method has been applied to couple the chemical kinetics and fluid dynamics and to capture effectively and accurately the steep gradient flame field. The pressure-velocity coupling is handled by two methodologies including the pressure-correction algorithm and the projection scheme. A stiff, operator-split projection scheme for the detailed nonequilibrium chemistry has been employed to treat the stiff reaction source terms. The conservative form of the governing equations are integrated over a cell-centered control volume with collocated storage for all transport variables. Computations using detailed chemistry and variable transport properties were performed for two laminar reacting flows: a counterflow hydrogen-air diffusion flame and a lifted methane-air triple flame. Numerical results favorably agree with measurements in terms of the detailed flame structure.

• Journal of Environmental Health Sciences
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• v.31 no.6
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• pp.489-497
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• 2005

A numerical method for the mathematical water modeling in 2-dimensional flow has been developed. The model based on a split operator technique, in which, the advection term is calculated using the upwind scheme. The diffusion term is one- dimensionalized and calculated using Crank-Nicholson's implicit finite difference scheme to reduce the numerical errors from large time steps and variable spacings. It also provides a relatively simple and economic method for more accurate simulation of pollutant dispersion. Water depths and flow velocities in the Boreyong reservoir during the normal water periods were predicted by numerical experiments with a 2-dimensional flow model so as to provide current field data for the study of advection and diffusion of pollutants. Developed 2-dimensional water quality model is applied to Boreyong reservoir to simulate a spatial and periodical changes of water quality.

• Journal of Korea Water Resources Association
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• v.30 no.2
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• pp.143-154
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• 1997

A numerical model for solving advection-diffusion equation is presented by splitoperator method combining the Holly-Preissmann scheme with a fifth-degree interpolating polynomial for advection operator and the explicit scheme porposed by Hobson et al. for diffusion operator. To examine the developed model, the obtained numerical solutions are compared with both the analytic solution and those from the existing models for the instantaneous source (Gaussian hill) and the continuous source (advanced front) at upstream boundary with constant velocity and diffusivity condition. For the various cases having different Courant and Peclet numbers, it is shown that the present study provides stable solutions even for Courant numbers exceeding one. The result obtained by the present study also agree well with existing analytical solutions for both cases. The proposed explicit scheme somewhat releases the conventional restriction of explicit schemes for determining the time step size and provides satisfactory results for relatively large time step size.

• Bulletin of the Korean Chemical Society
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• v.35 no.11
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• pp.3294-3298
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• 2014

We theoretically investigated the coherent control of Autler-Townes splitting in photoelectron spectroscopy of K2 molecule within an ultrafast laser pulse by solving the time-dependent Schrodinger equation using a quantum wave packet method. It was theoretically shown that we can manipulate the splitting of photoelectron spectroscopy by altering the laser intensity. Furthermore, it was found that the percentages of each peak in photoelectron spectroscopy can be controlled by changing the envelope of the laser pulse.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.2
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• pp.495-506
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• 2013

This study developed the Time-split Mixing Model (TMM) which can represent the pollutant mixing process on a three-dimensional open channel through constructing the conceptual model based on Taylor's assumption (1954) that the shear flow dispersion is the result of combination of shear advection and diffusion by turbulence. The developed model splits the 2-D mixing process into longitudinal mixing and transverse mixing, and it represents the 2-D advection-dispersion by the repetitive calculation of concentration separation by the vertical non-uniformity of flow velocity and then vertical mixing by turbulent diffusion sequentially. The simulation results indicated that the proposed model explains the effect of concentration overlapping by boundary walls, and the simulated concentration was in good agreement with the analytical solution of the 2-D advection-dispersion equation in Taylor period (Chatwin, 1970). The proposed model could explain the correlation between hydraulic factors and the dispersion coefficient to provide the physical insight about the dispersion behavior. The longitudinal dispersion coefficient calculated by the TMM varied with the mixing time unlike the constant value suggested by Elder (1959), whereas the transverse dispersion coefficient was similar with the coefficient evaluated by experiments of Sayre and Chang (1968), Fischer et al. (1979).

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.8
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• pp.47-54
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• 2006

In this paper, numerical algorithms applied in two-step eulerian scheme are investigated and implemented. Element quantities are advected with donor or van Leer algorithm. Nodal quantities are advected with Simplifed ALE [SALE] algorithm. Material interfaces are determined with Simple Line Interface Calculation [SLIC] algorithm. Practical aspects considered for code development are addressed in detail. The results of developed two-step Eulerian code are verified by comparing with those from pure lagrangian scheme and commercial code.