Level set methods: An overview and some recent results. (English) Zbl 0988.65093

The basic goal of the paper is to compare and analyze the subsequent motion of \(\Gamma\) under a velocity field \(v\) (depending on \(\Gamma\)).
The paper contains the key definitions and basic level set technology, as well as a few words about the numerical implementation. Moreover, recent variants, extensions and a rather interesting selection of related fast numerical methods are given. Applications of the moving interfaces in compressible, incompressible flows, Stefano problems, kinetic crystal growth, epitaxial growth of thin fibers, vertex-dominated flows, and extensions to multiphase motion are presented.
Reviewer: V.Dolejsi (Praha)


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76T30 Three or more component flows
80A22 Stefan problems, phase changes, etc.
35K55 Nonlinear parabolic equations
35R35 Free boundary problems for PDEs
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
82D25 Statistical mechanics of crystals


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