The Voronoi Implicit Interface Method for computing multiphase physics
Abstract
In this paper, 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. Finally, 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.
- Authors:
-
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); National Inst. of Health (NIH) (United States)
- OSTI Identifier:
- 1407108
- Grant/Contract Number:
- AC02-05CH11231; U54CA143833
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Proceedings of the National Academy of Sciences of the United States of America
- Additional Journal Information:
- Journal Volume: 108; Journal Issue: 49; Journal ID: ISSN 0027-8424
- Publisher:
- National Academy of Sciences, Washington, DC (United States)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; multiple interface dynamics; level set methods; foams; minimal surfaces
Citation Formats
Saye, Robert I., and Sethian, James A. The Voronoi Implicit Interface Method for computing multiphase physics. United States: N. p., 2011.
Web. doi:10.1073/pnas.1111557108.
Saye, Robert I., & Sethian, James A. The Voronoi Implicit Interface Method for computing multiphase physics. United States. https://doi.org/10.1073/pnas.1111557108
Saye, Robert I., and Sethian, James A. Mon .
"The Voronoi Implicit Interface Method for computing multiphase physics". United States. https://doi.org/10.1073/pnas.1111557108. https://www.osti.gov/servlets/purl/1407108.
@article{osti_1407108,
title = {The Voronoi Implicit Interface Method for computing multiphase physics},
author = {Saye, Robert I. and Sethian, James A.},
abstractNote = {In this paper, 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. Finally, 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.},
doi = {10.1073/pnas.1111557108},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 49,
volume = 108,
place = {United States},
year = {Mon Nov 21 00:00:00 EST 2011},
month = {Mon Nov 21 00:00:00 EST 2011}
}
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