期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 108, 期 49, 页码 19498-19503出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1111557108
关键词
multiple interface dynamics; level set methods; foams; minimal surfaces
资金
- Office of Energy Research, US Department of Energy [DE-AC02-05CH11231]
- Division of Mathematical Sciences of the National Science Foundation
- National Cancer Institute [U54CA143833]
- Miller Foundation at University of California, Berkeley
- Einstein Foundation, Berlin
- American Australian Association
We introduce a numerical framework, the Voronoi Implicit Interface Method for tracking multiple interacting and evolving regions (phases) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.), intricate jump conditions, internal constraints, and boundary conditions. The method works in two and three dimensions, handles tens of thousands of interfaces and separate phases, and easily and automatically handles multiple junctions, triple points, and quadruple points in two dimensions, as well as triple lines, etc., in higher dimensions. Topological changes occur naturally, with no surgery required. The method is first-order accurate at junction points/lines, and of arbitrarily high-order accuracy away from such degeneracies. The method uses a single function to describe all phases simultaneously, represented on a fixed Eulerian mesh. We test the method's accuracy through convergence tests, and demonstrate its applications to geometric flows, accurate prediction of von Neumann's law for multiphase curvature flow, and robustness under complex fluid flow with surface tension and large shearing forces.
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