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Comp."],"abstract":"<p>We propose a mathematical model for two-dimensional continua in order to establish a solid theoretical foundation for the study of their complex topology, large geometric deformations, and topological changes such as merging in the context of multiphase flows. Our modeling space, named the Yin space, consists of regular open semianalytic sets with bounded boundaries, and is further equipped with constructive and algebraic definitions of Boolean operations. Major distinguishing features of our model include (a) topological information of fluids such as Betti numbers can be easily extracted in constant time, (b) topological changes of fluids are captured by nonmanifold points on fluid boundaries, and (c) Boolean operations on fluids correctly handle all degenerate cases and apply to arbitrarily complex topologies, yet they are simple and efficient in that they only involve determining the relative position of a point to a Jordan curve and intersecting a number of curve segments. Finally, utilities of (a) and (c) are demonstrated by combining the Yin space with the recent cubic MARS method to track a complex fluid in a single vortex flow.<\/p>","DOI":"10.1090\/mcom\/3539","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T09:35:57Z","timestamp":1582709757000},"page":"2333-2364","source":"Crossref","is-referenced-by-count":8,"title":["Boolean algebra of two-dimensional continua with arbitrarily complex topology"],"prefix":"10.1090","volume":"89","author":[{"given":"Qinghai","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhixuan","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2020,5,8]]},"reference":[{"key":"1","series-title":"Wiley Series in Computational Mechanics","doi-asserted-by":"crossref","DOI":"10.1002\/9781118483565","volume-title":"Computational Fluid-structure Interaction: Methods and Applications","author":"Bazilevs, Y.","year":"2013"},{"key":"2","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1109\/TC.1979.1675432","article-title":"Algorithms for reporting and counting geometric intersections","volume":"C-28","author":"Bentley, J. 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