The Voronoi Implicit Interface Method for computing multiphase physics

Journal Article · Mon Nov 21 00:00:00 UTC 2011 · Proceedings of the National Academy of Sciences of the United States of America

DOI: https://doi.org/10.1073/pnas.1111557108 · OSTI ID:1407108

Saye, Robert I. ^[1]; Sethian, James A. ^[1]

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1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)

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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: National Inst. of Health (NIH) (United States); National Science Foundation (NSF) (United States); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1407108
• Journal Information: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 49 Vol. 108; ISSN 0027-8424
• Publisher: National Academy of Sciences, Washington, DC (United States)Copyright Statement
• Country of Publication: United States
• Language: English