• Journal of computational fluids engineering
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• v.4 no.1
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• pp.19-26
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• 1999

This paper describes a numerical method for predicting the incompressible unsteady laminar three-dimensional flows with free-surface. The Navier-Stokes equations governing the flows have been discretized by means of finite-difference approximations, and the resulting equations have been solved via the SIMPLE-C algorithm. The free-surface is defined by the motion of a set of marker particles and the interface behaviour was investigated by means of a "Lagrangian" technique. Using the GALA concept of Spalding, the conventional mass continuity equation is modified to form a volumetric or bulk-continuity equation. The use of this bulk-continuity relation allows the hydrodynamic variables to be computed over the entire flow domain including both liquid and gas regions. Thus, the free-surface boundary conditions are imposed implicitly and the problem formulation is greatly simplified. The numerical procedure is validated by comparing the predicted results of a periodic standing waves problems with analytic solutions. The results show that this numerical method produces accurate and physically realistic predictions of three-dimensional free-surface flows.

• Journal of computational fluids engineering
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• v.19 no.4
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• pp.20-28
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• 2014

An efficient solution algorithm for simulating free surface problem is presented. Navier-Stokes equations for variable density incompressible flow are employed as the governing equation on Cartesian meshes. In order to describe the free surface motion efficiently, VOF(Volume Of Fluid) method utilizing THINC(Tangent of Hyperbola for Interface Capturing) scheme is employed. The most time-consuming part of the current free surface flow simulations is the solution step of the linear system, derived by the pressure Poisson equation. To solve a pressure Poisson equation efficiently, the PCG(Preconditioned Conjugate Gradient) method is utilized. This study showed that the proper application of the preconditioner is the key for the efficient solution of the free surface flow when its pressure Poisson equation is solved by the CG method. To demonstrate the efficiency of the current approach, we compared the convergence histories of different algorithms for solving the pressure Poisson equation.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.2
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• pp.153-168
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• 2016

Sloshing phenomenon is a complicated free surface flow problem that increases the dynamic pressure on the sidewalls and the bottom of the storage tanks. When the storage tanks are partially filled, it is essential to be able to evaluate the fluid dynamic loads on the tank's perimeter. In this paper, a numerical code was developed to determine the pressure distribution on the rectangular and trapezoidal storage tanks' perimeters due to liquid sloshing phenomenon. Assuming the fluid to be inviscid, the Laplace equation and the nonlinear free surface boundary conditions were solved using coupled boundary element - finite element method. The code performance for sloshing modeling was validated using Nakayama and Washizu's results. Finally, this code was used for partially filled rectangular and trapezoidal storage tanks and free surface displacement, pressure distribution and horizontal and vertical forces exerted on the tanks' perimeters due to liquid sloshing phenomenon were estimated and discussed.

• Bulletin of the Society of Naval Architects of Korea
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• v.17 no.4
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• pp.13-20
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• 1980

The integral equation method to solve the boundary-value problem of a 2-dimensional body oscillating in the presence of a free surface generally breaks down at and near irregular frequencies due to the hypothetical flow inside the body. In this paper singularity distributions were extended to an inner free surface to remove the irregular frequency as Ohmatsu's work in 1978, and the solution for the above problem was found by using stream function. For various bodies including Lewis form cylinders, the hydrodynamic forces were calculated numerically at various wave numbers. From the results we concluded that the irregular frequencies can be removed even for the Lewis form cylinder as Ohmatsu done for circular cylinders, and calculated hydrodynamic forces by the present method are little higher than those of Ohmatsu's when the singularities are put on the inner free surface of the body. We specially point out that the solution for heaving motion converges in an oscillatory manner but not for swaying and rolling motions.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1997.04a
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• pp.128-135
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• 1997

The indirect boundary integral equation is formulated to analyze the behavior of a cavity in a multilayered half-plane subjected to earthquake waves. This formulation uses the fundamental solutions that are numerically calculated by the generalized transmission and reflection coefficient method. The free surface of the cavity without external excitation influences the behavior of the half-plane. Consequently this analysis adds the consideration of scattering-field into the analysis and the total motion field of the cavity is decomposed into the free-field and scattering-field motions. The free-field motion is obtained from the modification of the transmission and reflection coefficient method. The scattering-field motion is calculated is calculated by the indirect boundary value problem which has the ficticious boundaries and sources. In this study, P wave, SV wave, SH wave, and Rayleigh wave are analyzed respectively.

• Journal of the Society of Naval Architects of Korea
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• v.51 no.4
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• pp.265-273
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• 2014

Wave-body interaction is simulated using a developed code based on the flux-difference splitting scheme for immiscible and incompressible fluids and the hybrid Cartesian/immersed boundary method. A free surface is captured as a moving contact discontinuity within a fluid domain and an approximated Riemann solver is used to estimate the inviscid flux across the discontinuity. Immersed boundary nodes are identified inside an instantaneous fluid domain near a moving body, then dependent variables are reconstructed at those immersed boundary nodes based on interpolation along local normal lines to the boundary. Free surface flows around an oscillating cylinder are simulated and the computed wave elevations are compared with other reported results. The generation of a solitary wave by a moving wave-maker is simulated and the time histories of wave elevations at two different points are compared with other results. The developed code is applied to simulate body motion of an elastically mounted circular cylinder as a solitary wave passes the body. The force acting on an elastically mounted cylinder is compared with the force acting on a fixed cylinder. Grid independency of the computed body motion is established based on a comparison of results using three different-size grids.

• Journal of the Korean Society of Visualization
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• v.9 no.4
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• pp.74-79
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• 2011

In this study the change of free surface vortex is represented at different times according to height of water and with or without curtain wall installation. The air volume fraction is investigated at each condition of water level and the influence about creation of vortex is analyzed. The height of sump intake is taken as 100mm and the water level is divided into 5 steps. The sump model is the TSJ model and the curtain wall is applied by HI standard of America. The results shows that the free surface vortex can be identified on the isotropic surface at air volume fraction 1%~5% and the vortices make an air column from the free surface to the sump intake and are created and destroyed repeatedly. In the higher water level, less air is absorbed into the intake pipe. After curtain wall installation, the suction rate of the air volume fraction is decreased by 6.7%. The result of the vortex motion according to time, works on a cycle.

• Journal of the Society of Naval Architects of Korea
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• v.43 no.6 s.150
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• pp.667-674
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• 2006

Accurate prediction of ship dynamics, particularly roll motion, is very important in ship safety. In the past, empirical or vortex based methods were commonly used for the hydrodynamic roll damping predictions but they could not be applied to practical ship roll motion cause of limitations about geometries ad design conditions. Recently RANS-based techniques are developed for the practical ship motion analysis. In this study, RANS based roil analysis about a rectangular cylinder with WAVIS developed by MOERI/KORDI are performed and compared with the experimental data and other RANS results.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.188-192
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• 2004

A Numerical analysis method is developed in order to compute the flaw and wave field for 2-dimensional floating body in the free roll motion with 3 degrees of freedom. Navier-Stokes and continuity equations are gaverning equations in tire present study. Finite Difference method is introduced to discretize the governing equation. The free surface is traced by the interface tracking method and the grid system is fitted to boundaries including free surface and body surface, which is moving in the flow field. The numerical scheme is based on Maker and Cell method. For the sake of validation of the numerical method, the computed roll decay factors according to tire midship section shapes are compared with measured results. The numerical results are discussed in order to understand the effect of midship section shape on roll motion.

• Geophysics and Geophysical Exploration
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• v.15 no.2
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• pp.92-101
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• 2012

Three-dimensional finite-difference simulation in a small-scale half-sphere basin with planar free-surface is performed for an arbitrary shear-dislocation point source. A new scheme to deal with free-surface boundary condition is presented. Then basin parameters are examined to understand main characteristics on ground-motion response in the basin. To analyze the frequency content of ground motion in the basin, spectral amplitudes are compared with each other for four sites inside and outside the basin. Also particle motions for those sites are examined to find which kind of wave plays a dominant role in ground-motion response. The results show that seismic energy is concentrated on a marginal area of the basin far from the source. This focusing effect is mainly due to constructive interference of the direct Swave with basin-edge induced surface waves. Also, ground-motion amplification over the deepest part of the basin is relatively lower than that above shallow basin edge. In the small-scale basin with relatively simple bedrock interface, therefore, the ground-motion amplification may be more related to the source azimuth or direction of the incident waves into the basin rather than depth of it.