HFES: A Height Function Method with Explicit Input and Signed Output for High-Order Estimations of Curvature and unit Vectors of Planar Curves

DOI10.1137/15M105001XzbMath1362.65028MaRDI QIDQ5347530

Qinghai Zhang

Publication date: 24 May 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

surface tensioncurvature estimationshape analysisheight functionregular open setsoriented Jordan curves

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Liquid-gas two-phase flows, bubbly flows (76T10) Numerical differentiation (65D25)

Related Items (5)

Fourth- and Higher-order Interface Tracking Via Mapping and Adjusting Regular Semianalytic sets Represented by Cubic Splines ⋮ A hybrid inference system for improved curvature estimation in the level-set method using machine learning ⋮ Parabolic interface reconstruction for 2D volume of fluid methods ⋮ Boolean algebra of two-dimensional continua with arbitrarily complex topology ⋮ Height-function curvature estimation with arbitrary order on non-uniform Cartesian grids

Uses Software

• Gerris
• PROST
• MARS
• GePUP

Cites Work

• On the properties and limitations of the height function method in two-dimensional Cartesian geometry
• An improved height function technique for computing interface curvature from volume fractions
• A mesh-decoupled height function method for computing interface curvature
• An accurate adaptive solver for surface-tension-driven interfacial flows
• Second-order accurate normals from height functions
• On reducing interface curvature computation errors in the height function technique
• Compact finite difference schemes with spectral-like resolution
• Modelling merging and fragmentation in multiphase flows with SURFER
• A new algorithm for dominant points detection and polygonization of digital curves.
• PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method.
• A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles.
• GePUP: generic projection and unconstrained PPE for fourth-order solutions of the incompressible Navier-Stokes equations with no-slip boundary conditions
• Efficient simulation of surface tension-dominated flows through enhanced interface geometry interrogation
• Interface curvature via volume fractions, heights, and mean values on nonuniform rectangular grids
• MARS: An Analytic Framework of Interface Tracking via Mapping and Adjusting Regular Semialgebraic Sets
• A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation
• Fourth-Order Interface Tracking in Two Dimensions via an Improved Polygonal Area Mapping Method
• High-order Techniques for Calculating Surface Tension Forces
• Shape Classification and Analysis
• Elementary Differential Geometry
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