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Title: 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:
 [1];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); 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. doi:10.1073/pnas.1111557108.
Saye, Robert I., and Sethian, James A. Mon . "The Voronoi Implicit Interface Method for computing multiphase physics". United States. doi: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 = {2011},
month = {11}
}

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