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논문 기본 정보
- 자료유형
- 학술대회자료
- 저자정보
- 발행연도
- 2009.5
- 수록면
- 81 - 91 (11page)
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초록· 키워드
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We present a level set method on non-graded adaptive Cartesian grids, i.e. grids for which the ratio between adjacent cells is not constrained. We use quadtree and octree data structures to represent the grid and a simple algorithm to generate a mesh with the finest resolution at the interface. In particular, we present (1) a locally third order accurate reinitialization scheme that transforms an arbitrary level set function into a signed distance function, (2) a second order accurate semi-Lagrangian methods to evolve the linear level set advection equation under an externally generated velocity field, (3) a second order accurate upwind method to evolve the non-linear level set equation under a normal velocity as well as to extrapolate scalar quantities across an interface in the normal direction, and (4) a semi-implicit scheme to evolve the interface under mean curvature. Combined, we obtain a level set method on adaptive Cartesian grids with a negligible amount of mass loss. We propose numerical examples in two and three spatial dimensions to demonstrate the accuracy of the method.
목차
ABSTRACT
INTRODUCTION
1. THE LEVEL SET METHOD
2. SPATIAL DISCRETIZATION AND REFINEMENT CRITERION
3. FINITE DIFFERENCE DISCRETIZATIONS
4. INTERPOLATION PROCEDURES
5. REINITIALIZATION SCHEME
6. MOTION UNDER AN EXTERNALLY GENERATED VELOCITY FIELD
7. MOTION IN THE NORMAL DIRECTION AND CURVATURE DRIVEN FLOW
8. CONCLUSION
REFERENCES
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UCI(KEPA) : I410-ECN-0101-2012-410-003697066