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We propose a mathematical model for fluids in multiphase flows in order toestablish a solid theoretical foundation for the study of their complextopology, large geometric deformations, and topological changes such asmerging. Our modeling space consists of regular open semianalytic sets withbounded boundaries, and is further equipped with constructive and algebraicdefinitions of Boolean operations. Major distinguishing features of our modelinclude (a) topological information of fluids such as Betti numbers can beeasily extracted in constant time, (b) topological changes of fluids arecaptured by non-manifold points on fluid boundaries, (c) Boolean operations onfluids correctly handle all degenerate cases and apply to arbitrarily complextopologies, yet they are simple and efficient in that they only involvedetermining the relative position of a point to a Jordan curve and intersectinga number of curve segments. Although the main targeting field is multiphaseflows, our theory and algorithms may also be useful for related fields such assolid modeling, computational geometry, computer graphics, and geographicinformation system.

Fluid Modeling and Boolean Algebra for Arbitrarily Complex Topology in Two Dimensions