期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 54, 期 2-3, 页码 369-413出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-012-9660-1
关键词
Elliptic; Parabolic; Level-set method; Poisson; Diffusion; Stefan; Quadtree; Octree; Ghost-fluid method
资金
- ONR [N00014-11-1-0027, N00014-09-1-0101, ONR N-00014-11-1-0027]
- NSF [CHE 1027817]
- DOE [DE-FG02-08ER15991]
- ICB [W911NF-09-D-0001]
- W.M. Keck Foundation
- Priority Research Centers Program through the National Research Foundation of Korea (NRF)
- Ministry of Education, Science and Technology [20100028298]
- Korea Research Foundation
- Korean Government [KRF-2011-0013649]
- ARL AHPCRC [W911NF-07-0027, NSF IIS-1048573]
- Intel Science and Technology Center for Visual Computing
We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree node-based adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.
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