• Title/Summary/Keyword: level set method

### A multiple level set method for modeling grain boundary evolution of polycrystalline materials

• Zhang, Xinwei;Chen, Jiun-Shyan;Osher, Stanley
• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.191-209
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• 2008
• In this paper, we model grain boundary evolution based on a multiple level set method. Grain boundary migration under a curvature-induced driving force is considered and the level set method is employed to deal with the resulting topological changes of grain structures. The complexity of using a level set method for modeling grain structure evolution is due to its N-phase nature and the associated geometry compatibility constraint. We employ a multiple level set method with a predictor-multicorrectors approach to reduce the gaps in the triple junctions down to the grid resolution level. A ghost cell approach for imposing periodic boundary conditions is introduced without solving a constrained problem with a Lagrange multiplier method or a penalty method. Numerical results for both uniform and random grain structures evolution are presented and the results are compared with the solutions based on a front tracking approach (Chen and Kotta et al. 2004b).

### Level set method for the simulation of rising bubble based on triangular and Quadrilateral elements (삼각형 요소와 사각형 요소에 기초한 상승기포의 모사를 위한 Level set 방법)

• Cho, M.H.;Choi, H.G.;Jeon, B.J.;Yoo, J.Y.
• 한국전산유체공학회:학술대회논문집
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• pp.10-13
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• 2011
• A level set method is proposed to simulate the incompressible two-phase flow considering the effect of surface tension. For reinitialization of level set junction, a direct approach method is employed, instead of solving hyperbolic type equation. A mixed element is adopted, so that the continuity mid Navier-Stokes equations are solved by using the quadratic elements (six-node triangular element mid nine-node quadrilateral element), mid the level set function is solved by using the linear elements (three-node triangular element mid four-node quadrilateral element). In order to verify the accuracy mid robustness of the codes, the present methods are applied to a few benchmark problems. It is confirmed that the present results are in good qualitative mid quantitative agreements with the existing studies.

### Topology Optimization of Shell Structures Using Adaptive Inner-Front Level Set Method (AIFLSM) (적응적 내부 경계를 갖는 레벨셋 방법을 이용한 쉘 구조물의 위상최적설계)

• Park, Kang-Soo;Youn, Sung-Kie
• Proceedings of the KSME Conference
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• pp.354-359
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• 2007
• A new level set based topology optimization employing inner-front creation algorithm is presented. In the conventional level set based topology optimization, the optimum topology strongly depends on the initial level set distribution due to the incapability of inner-front creation during optimization process. In the present work, an inner-front creation algorithm is proposed, in which the sizes, positions, and number of new inner-fronts during the optimization process can be globally and consistently identified. To update the level set function during the optimization process, the least-squares finite element method is employed. As demonstrative examples for the flexibility and usefulness of the proposed method, the level set based topology optimization considering lightweight design of 3D shell structure is carried out.

### Extension of Fast Level Set Method with Relationship Matrix, Modified Chan-Vese Criterion and Noise Reduction Filter

• Vu, Dang-Tran;Kim, Jin-Young;Choi, Seung-Ho;Na, Seung-You
• The Journal of the Acoustical Society of Korea
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• v.28 no.3E
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• pp.118-135
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• 2009
• The level set based approach is one of active methods for contour extraction in image segmentation. Since Osher and Sethian introduced the level set framework in 1988, the method has made the great impact on image segmentation. However, there are some problems to be solved; such as multi-objects segmentation, noise filtering and much calculation amount. In this paper we address the drawbacks of the previous level set methods and propose an extension of the traditional fast level set to cope with the limitations. We introduce a relationship matrix, a new split-and-merge criterion, a modified Chan-Vese criterion and a novel filtering criterion into the traditional fast level set approach. With the segmentation experiments we evaluate the proposed method and show the promising results of the proposed method.

### Multi-Phase Flows and Image Processing: Level Set Method (다상유체와 영상처리 : 레벨셋 방법)

• Kang, M.J.
• 한국전산유체공학회:학술대회논문집
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• pp.259-260
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• 2011
• Using modern techniques from scientific computing and numerical analysis, natural phenomena or scientific experiment can be simulated effectively with a computer and used for computer graphics, for example as special effects for the film industry, manufacturing the thin film, multi-phase simulation and image processing. The Level Set method can make those things happen without a lot of difficulties. This method was devised by Osher and Sethian(1988) to represent dynamically moving interfaces as the zero level set of a scalar function that evolves in time. Since then, many researchers have worked on many applications using a Level Set Method. I will give a talk about the applications of the Level Set Method.

### An Edge Profile Adaptive Bi-directional Diffusion Interpolation

• Kim, Bong-Joe;Sohn, Kwang-Hoon
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• v.16 no.3
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• pp.501-509
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• 2011
• In this paper, we propose an edge profile adaptive bi-directional diffusion interpolation method which consists of shock filter and level set. In recent years many interpolation methods have been proposed but all methods have some degrees of artifacts such as blurring and jaggies. To solve these problems, we adaptively apply shock filter and level set method where shock filter enhances edge along the normal direction and level set method removes jaggies artifact along the tangent direction. After the initial interpolation, weights of shock filter and level set are locally adjusted according to the edge profile. By adaptive coupling shock filter with level set method, the proposed method can remove jaggies artifact and enhance the edge. Experimental results show that the average PSNR and MSSIM of our method are increased, and contour smoothness and edge sharpness are also improved.

### Study on the Finite Element Discretization of the Level Set Redistancing Algorithm (Level Set Redistancing 알고리즘의 유한요소 이산화 기법에 대한 연구)

• Kang Sungwoo;Yoo Jung Yul;Lee Yoon Pyo;Choi HyoungGwon
• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.6
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• pp.703-710
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• 2005
• A finite element discretization of the advection and redistancing equations of level set method has been studied. It has been shown that Galerkin spatial discretization combined with Crank-Nicolson temporal discretization of the advection equation of level set yields a good result and that consistent streamline upwind Petrov-Galerkin(CSUPG) discretization of the redistancing equation gives satisfactory solutions for two test problems while the solutions of streamline upwind Petrov-Galerkin(SUPG) discretization are dissipated by the numerical diffusion added for the stability of a hyperbolic system. Furthermore, it has been found that the solutions obtained by CSUPG method are comparable to those by second order ENO method.

### An Interface Tracking Scheme based on VOF Coupled with Level Set Method (Level Set 방법과 결합된 VOF 기반의 경계면 추적법)

• Suh, Young-Ho;Son, Gi-Hun
• Proceedings of the KSME Conference
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• pp.113-118
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• 2001
• We present a new interface tracking method for computing two-phase flow. This method is based on VOF method coupled with Level set method. The method is verified to calculate an interfacial curvature accurately as well as to achieve volume conservation during the whole computation period. We apply the present method to calculate a falling drop. The calculated shape and terminal velocity of the falling drop showed good agreement with the data reported in the literature. Also, the present method was proven to be applicable to drop-wall collision phenomenon.

### Numerical Study of Droplet Impact on Solid Surfaces Using a Coupled Level Set and Volume-of-Fluid Method (CLSVOF 방법을 이용한 액적-벽면 충돌에 관한 수치적 연구)

• Suh, Young-Ho;Son, Gi-Hun
• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.744-752
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• 2003
• A level set method is combined with the volume-of-fluid method so that the coupled method can not only calculate an interfacial curvature accurately but also can achieve mass conservation well. The coupled level set and volume-of-fluid(CLSVOF) method is efficiently implemented by employing an interface reconstruction algorithm which is based on the explicit relationship between the interface configuration and the fluid volume function. The CLSVOF method is applied for numerical simulation of droplet impact on solid surfaces with variable contact angles. The numerical results are found to preserve mass conservation and to be in good agreement with the data reported in the literature. Also, the present method proved to be applicable to the complex phenomena such as breakup and rebound of a droplet.

### Application of a fixed Eulerian mesh-based scheme based on the level set function generated by virtual nodes to large-deformation fluid-structure interaction

• Hashimoto, Gaku;Ono, Kenji;Okuda, Hiroshi
• Interaction and multiscale mechanics
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• v.5 no.3
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• pp.287-318
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• 2012
• We apply a partitioned-solution (iterative-staggered) coupling method based on a fixed Eulerian mesh with the level set function to a large-deformation fluid-structure interaction (FSI) problem where a large-deformable thin structure moves in a high-speed flow field, as an airbag does during deployment. This method combines advanced fluid and structure solvers-specifically, the constrained interpolation profile finite element method (CIP-FEM) for fluid Eulerian mesh and large-deformable structural elements for Lagrangian structural mesh. We express the large-deformable interface as a zero isosurface by the level set function, and introduce virtual nodes with level sets and structural normal velocities to generate the level set function according to the large-deformable interfacial geometry and enforce the kinematic condition at the interface. The virtual nodes are located in the direction normal to the structural mesh. It is confirmed that application of the method to unfolded airbag deployment simulation shows the adequacy of the method.