On generalized donating regions: classifying Lagrangian fluxing particles through a fixed curve in the plane

DOI10.1016/j.jmaa.2014.11.043zbMath1326.53010OpenAlexW2083548344MaRDI QIDQ482728

Qinghai Zhang

Publication date: 6 January 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.11.043

zbMATH Keywords

winding numberHopf theoremcycle decompositionflux setgeneralized donating regionsstreakline

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Nonautonomous smooth dynamical systems (37C60) Kinematics of a particle (70B05)

Related Items (7)

Fourth- and Higher-order Interface Tracking Via Mapping and Adjusting Regular Semianalytic sets Represented by Cubic Splines ⋮ Boolean algebra of two-dimensional continua with arbitrarily complex topology ⋮ Lagrangian Transport through Surfaces in Compressible Flows ⋮ A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows ⋮ Lagrangian Transport Through Surfaces in Volume-Preserving Flows ⋮ MARS: An Analytic Framework of Interface Tracking via Mapping and Adjusting Regular Semialgebraic Sets ⋮ Lagrangian Flux Calculation Through a Fixed Planar Curve for Scalar Conservation Laws

Uses Software

• SADoRe

Cites Work

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• Polygons: Meister was right and Poinsot was wrong but prevailed
• Highly accurate Lagrangian flux calculation via algebraic quadratures on spline-approximated donating regions
• On Donating Regions: Lagrangian Flux through a Fixed Curve
• On a Family of Unsplit Advection Algorithms for Volume-of-Fluid Methods
• Rotation and Winding Numbers for Planar Polygons and Curves

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