• Transactions of the Korean Society of Mechanical Engineers B
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• v.32 no.10
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• pp.754-760
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• 2008

Computation of moving interface by the level set method typically requires the reinitialization of level set function. An inaccurate estimation of level set function $\phi$ results in incorrect free-surface capturing and thus errors such as mass gain/loss. Therefore, an accurate and robust reinitialization process is essential to the simulation of free-surface flows. In the present paper, we pursue further development of the reinitialization process, which evaluates level set function directly using a normal vector on the interface without solving there-distancing equation of hyperbolic type. The Taylor-Galerkin approximation and P1P1 splitting/SUPG (Streamline Upwind Petrov-Galerkin) FEM are adopted to discretize advection equation of the level set function and the incompressible Navier-Stokes equation, respectively. Advection equation and re-initialization process of free surface capturing are validated with benchmark problems, i.e., a broken dam flow and timereversed single vortex flow. The simulation results are in good agreement with the existing results.

• Ocean Systems Engineering
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• v.2 no.3
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• pp.229-238
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• 2012

We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

• Proceedings of the KIEE Conference
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• 1987.07a
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• pp.311-315
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• 1987

In this paper an efficient algorithm to estimate the volume and surface area and the reconstruction algorithm for 3-dimensional graphics are presented. The graph theory is used to estimate the optimal quantitative factors. To improve the computing efficiency, the algorithm to get proper contour points is performed by applying several tolerances. The search and the given arc cost is limited according to the change of curvature of the cross-sectional contour. For mathematical model, these algorithms for volume estimation based on polyhedral approximation are applied to the selected optimal surface. The results show that the values of the volume and surface area for tolerances 1.0005, 1.001 and 1.002 approximate to values for tolerances 1.000 resulting in small errors. The reconstructed three-dimensional images are sparse and consist of larger triangular tiles between two cross sections as tolerance is increasing.

• The Transactions of the Korea Information Processing Society
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• v.6 no.9
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• pp.2504-2511
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• 1999

This paper proposes the scattered data interpolation as an efficient method that is designed for free-form surface. Data interpolation is an essential method of designing for various objects. For the generating free-form surface of complexity construction, the existing method had problems to represent flat area and sharp corner edge, in presenting objects with computing the weight of control points. For solving this problem, we proposes the generating method of new approximation surfaces, using scattered data interpolation. This method obtains B-Spline basis function which calculates main curvature, having optimized value in variable area, on given control points and changed objects, and then computes the changing rate the approximating data, using it's value. We also present this method that generates smoother free-form surface, using the scattered data interpolation with minimum weight.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.1
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• pp.95-104
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• 2002

Numerical solution of the full Navier-Stokes equation as well as the energy equation has been obtained for the unsteady natural convection in a rectangular enclosure. One side wall was maintained at very high temperature simulating fires. Especially the effect of surface radiation was taken into account. While the enclosed air was assumed to be transparent, the internal walls directly interacted one another through the surface radiation. Due to a significant temperature difference in the flow field, the equation of state was used instead of the Boussinesq approximation. It was found that the rapid heating of the adiabatic ceiling and floor by the incoming radiation from the hot wall made the evolution at thermo-fluid field highly unstable in the initial period. Therefore, the secondary cells brought about at the floor region greatly affected the heat transfer mechanism inside the enclosure. The heat transfer rate was augmented by the radiation, resulting in requiring less time for the flow to reach the steady state. At the steady state neglecting radiation two internal hydraulic jumps were clearly observed in upper/left as well as in lower/right comer. However, the hydraulic jump in the lower/right comer could not be observed for the case including radiation due to its high momentum flow over the bottom wall. Radiation resulted in a faster establishment of the steady state phenomena.

• Journal of Magnetics
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• v.7 no.4
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• pp.132-137
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• 2002

The electronic structures and magnetism of the non-oxide perovskite MgCFe$_3$(001) surface were investigated by using the all-electron full-potential linearized augmented plane wave (FLAPW) method within the generalized gradient approximation (GGA). We considered both of the MgFe terminated (MgFe-Term) and the CFe terminated (CFe-Term) surfaces. We found that the minority spin d-bands of Fe(S) of the MgFe-Term are strongly localized and Fermi level (EF) lies just below the sharp peak of the minority spin d-band of Fe(S), while the minority spin d-bands of Fe(S) of the CFe-Term are not localized much and Fermi level (E$_F$) lies in the middle of two peaks of the minority spins. The majority Fe(S) d-band width of MgFe- Term is narrower than that of the CFe-Term. It is found that the magnetic moment of Fe(S) of the MgFe- Term is 2.51 ${\mu}$$_B$, which is much larger than that of 1.97 ${\mu}$$_B$ of the CFe-Term.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.4
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• pp.123-130
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• 2018

Triangulation is one of the fundamental problems in computational geometry and computer graphics community, and it has huge application areas such as 3D printing, computer-aided engineering, surface reconstruction, surface visualization, and so on. The Delaunay refinement algorithm is a well-known method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. In this paper, we propose a simple but efficient algorithm to triangulate Voronoi surfaces of Voronoi diagram of spheres in 3-dimensional Euclidean space. The proposed algorithm is based on the Ruppert's Delaunay refinement algorithm, and we modified the algorithm to be applied to the triangulation of Voronoi surfaces in two ways. First, a new method to deciding the location of a newly added vertex on the surface in 3-dimensional space is proposed. Second, a new efficient but effective way of estimating approximation error between Voronoi surface and triangulation. Because the proposed algorithm generates a triangular mesh for Voronoi surfaces with guaranteed quality, users can control the level of quality of the resulting triangulation that their application problems require. We have implemented and tested the proposed algorithm for random non-intersecting spheres, and the experimental result shows the proposed algorithm produces quality triangulations on Voronoi surfaces satisfying the quality criterion.

• Journal of the Korean Geotechnical Society
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• v.24 no.12
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• pp.65-73
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• 2008

In the current practice for slope stability problem in Japan, the shear strength, $\tau$, mobilized along the failure surface is usually estimated based on an empirical approximation in which the cohesion, c, is assumed to be equal to the soil thickness above the supposed slip surface, d(m). This approximation is advantageous in that the result of stability analysis is not influenced by the designers in charge. However, since the methodology has little theoretical background, the cohesion may often be grossly overestimated, and conversely the angle of shear resistance, $\phi$, is significantly underestimated, when the soil thickness above the supposed slip surface is quite large. In this paper, a case record of natural slope failure that took place in Hyogo Prefecture in 2007, is described in detail for the case in which the shear strength along the collapsed surface was carefully examined in a series of direct shear box (DSB) tests by considering the effects of in-situ shear stress along the slip surface. It is demonstrated that the factor of safety agrees with that of in-situ conditions when the shear strength from this kind of DSB test was employed for the back-analysis of the slope failure.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.7
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• pp.71-79
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• 2002

A new rapid prototyping process, Variable Lamination Manufacturing using a 4-axis-controlled hotwire cutter and expandable polystyrene foam sheet as a laminating material of the part (VLM-S), has been developed to reduce building time and to improve the surface finish of parts. The objective of this study is to reconstruct the surface of the original 3D CAD model in order to generate mid-slice data using the advancing front technique. The generation of 3D layers by a 4 axis-controlled hot-wire cutter requires a completely different procedure to generate toolpath data unlike the conventional RP CAD systems. The cutting path data for VLM-S are created by VLM-Slicer, which is a special CAD/CAM software with automatic generation of 3D toolpath. For the conventional sheet type system like LOM, the STL file would be sliced into 2D data only. However, because of using the thick layers and a sloping edge with the firstorder approximation between the top and bottom layers, VLM-Slicer requires surface reconstruction, mid-slice, and the toolpath data generation as well as 2D slicing. Surface reconstruction demands the connection between the two neighboring cross-sectional contours using the triangular facets. VLM-S employs thick layers with finite thickness, so that surface reconstruction is necessary to obtain a sloping angle of a side surface and the point data at a half of the sheet thickness. In the process of the toolpath data generation the surface reconstruction algorithm is expected to minimize the error between the ruled surface and the original parts..

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.12
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• pp.1555-1569
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• 2000

Numerical simulation of fluid flow with moving free surface has been carried out. For the free surface flow, a VOF(Volume of Fluid)-based algorithm utilizing a fixed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface tracking algorithm based on the donor-acceptor scheme has been presented. Novel features of the proposed algorithm are characterized as two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems that are usual in finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3-D free surface flow problem without additional efforts. For computation of unsteady incompressible flow, a finite element approximation based on the explicit fractional step method has been adopted. In addition, the SUPG(streamline upwind/Petrov-Galerkin) method has been implemented to deal with convection dominated flows. Combination of the proposed free surface tracking scheme and explicit fractional step formulation resulted in an efficient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems.