• Journal of the Society of Naval Architects of Korea
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• v.29 no.3
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• pp.117-124
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• 1992

Waves around a practical hull form and a series 60 model are computed by rectangular variable spacing and staggered flesh systems based on MAC(Marker and Cell) method. As a governing equation, the Euler equation is adopted. The comparison indicates that the computed waves are in good agreement with the measured results and that the MAC method is useful. On the other hand, a critical condition for the appearance of sub-breaking waves derived from the in viscid instability analysis is applied to the calculated flow field around a blunt bow. It is confirmed that the derived condition detects well the appearance of sub-breaking waves.

• Journal of Ocean Engineering and Technology
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• v.12 no.2 s.28
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• pp.79-86
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• 1998

A three-dimensional WIG (Wing In Ground effect) moving above free surface is numerically studied by means of finite difference techniques. The air flow field around the WIG is analyzed by MAC (Marker & Cell) method, and interactions between WIG and the free surface are appeared as the variation of pressure distribution acting on the free surface. To analyze the wavemaking phenomena by those pressure distributions, the NS (Navier-Stokes) solver is employed in which nonlinearities of the free surface conditions can be included. Through the numerical simulation, Cp values and lift/drag ratio are carefully reviewed by changing the height/chord ratio. The section shape of model is NACA0012 with the span/chord ratio of 3.0. Through computational results, it is confirmed that the effect of free surface is small enough to treat it as a rigid wavy wall.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2061-2067
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• 2005

In this study, we focus on the submerged plate built into the Very Large Floating Structure with the partial openings of Sm long, which enables the reverse flow of incident wave to generate the wave breaking. The purpose of this study is to investigate the characteristics of wave exciting forces acting on the submerged plate and the fore part of VLFS. Firstly, we have carried out the extensive experiments to understand the characteristics of the wave exciting forces. Then we have performed the numerical simulations by applying the Marker and Cell method (MAC method) and compared with the experimental results. We discuss the validity of MAC method and the effects of the submerged plate on the motion of VLFS. As a result, we get the conclusion that the submerged plate is useful for reducing the wave exciting forces acting on the structure behind the submerged plate.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.2
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• pp.89-107
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• 2017

In this paper, we have proposed a modified Marker-And-Cell (MAC) method to investigate the problem of an unsteady 2-D incompressible flow with heat and mass transfer at low, moderate, and high Reynolds numbers with no-slip and slip boundary conditions. We have used this method to solve the governing equations along with the boundary conditions and thereby to compute the flow variables, viz. u-velocity, v-velocity, P, T, and C. We have used the staggered grid approach of this method to discretize the governing equations of the problem. A modified MAC algorithm was proposed and used to compute the numerical solutions of the flow variables for Reynolds numbers Re = 10, 500, and 50000 in consonance with low, moderate, and high Reynolds numbers. We have also used appropriate Prandtl (Pr) and Schmidt (Sc) numbers in consistence with relevancy of the physical problem considered. We have executed this modified MAC algorithm with the aid of a computer program developed and run in C compiler. We have also computed numerical solutions of local Nusselt (Nu) and Sherwood (Sh) numbers along the horizontal line through the geometric center at low, moderate, and high Reynolds numbers for fixed Pr = 6.62 and Sc = 340 for two grid systems at time t = 0.0001s. Our numerical solutions for u and v velocities along the vertical and horizontal line through the geometric center of the square cavity for Re = 100 has been compared with benchmark solutions available in the literature and it has been found that they are in good agreement. The present numerical results indicate that, as we move along the horizontal line through the geometric center of the domain, we observed that, the heat and mass transfer decreases up to the geometric center. It, then, increases symmetrically.

• Journal of Navigation and Port Research
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• v.28 no.7
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• pp.641-645
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• 2004

In this study, we focus on the submerged plate built into the Very Large Floating Structure with the partial openings of 5m long, which enables the reverse flow of incident wave to generate the wave breaking. The purpose of this study is to investigate the characteristics of wave exciting forces acting on the submerged plate. Firstly, we have carried out the extensive experiments to understand the characteristics of the wave exciting forces. Then we have performed the numerical simulations by applying the Marker and Cell method and compared with the experimental results. We discuss the validity of MAC method and the effects of the submerged plate on the motion of VLFS.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2004.04a
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• pp.203-207
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• 2004

In this study, we focus on the submerged plate built into the Very Large Floating Structure with the partial openings of 5m long, which enables the reverse flow of incident wave to generate the wave breaking. The purpose of this study is to investigate the characteristics of wave exciting forces acting on the submerged plate. Firstly, we have carried out the extensive experiments to understand the characteristics of the wave exciting forces. Then we have performed the numerical simulations by applying the Marker and Cell method and compare with the experimental results. We discuss the validity of MAC method and the effects of the submerged plate on the motion of VLFS.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.55-63
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• 1996

Numerical computations are carried out to analyze the characteristics of flow fields around Air Supported Ships. The computations are performed in a rectangular grid system based on MAC(Marker And Cell) method. The governing equations are represented in finite difference forms by forward differencing in time and centered differencing in space except for its convection terms. For the certification of this numerical analysis method, the computations of flow fields around a Catamaran, an ACV(Air Cushion Vehicle) modeled with pressure distribution on free surface and two SES(Surface Effect Ship)'s are carried out, The results of the present computations are compared with the previously presented computational and experimental results in the same condition.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.195-199
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• 2005

Wave breaking phenomenon near the fore body of a ship is numerically simulated. The ship advance with uniform velocity in calm water. For the simulation, incompressible Navier-Stokes equations and continuity equation are adopted as governing equations. The simulation is carried out in staggered variable mesh system with finite difference method. Marker and Cell(MAC) method and Marker-Density method are employed to track the free surface. Body boundary conditions are satisfied with the adoption of porosity method and no-slip condition on the hull surface. The ship model has a wedge type fore-body, and the computational domain is an appropriate region around the fore-body. The computation results are compared with some experimental results. Also the difference of the free surface tracking methods are discussed.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.138-147
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• 1995

The boundary conditions for the free-surface including the important meaning for both scientific and engineering purposes are described together with the numerical techniques to implement the conditions. Two kinds of numerical method based on MAC method are introduced. One is applied to the problem of 2D solitary wave propagation and the other is applied to the problem of 3D bow wave breaking.

• Journal of Ocean Engineering and Technology
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• v.16 no.2
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• pp.1-5
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• 2002

In the past, ports have been mainly developed in natural harbors but nowadays ports are built wherever they can be economically justified. Therefore, construction of breakwater in area that establishment of structure is disadvantageous is risen according to the change of conditions to the location for ports. In case of building gravity breakwater in such point, need that plane shapes of more reasonable section permitting wave overtopping is necessary. One of the earliest methods for solving unsteady incompressible flow including free surfaces is the MAC(Marker And Cell) method by Harlow and Welch (1965). Recently. VOF(Volume Of Fluid) method to improve several drawbacks of MAC method is suggested by Hirt and Nichols(1981) and utilized extensively in fields of hydrodynamics. Wave overtopping phenomenon is simulated including wave breaking for permeable breakwater by numerical analysis and investigated features of wave overtopping behind structure using VOF method.