Meshless Helmholtz-Hodge Decomposition

Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. This decompo...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics 2010-03, Vol.16 (2), p.338-349
Main Authors: Petronetto, F., Paiva, A., Lage, M., Tavares, G., Lopes, H., Lewiner, T.
Format: Article
Language:English
Subjects:
Algorithms
Application software
Computational fluid dynamics
Computational modeling
Computer Graphics
Computer Simulation
Decomposition
Feature extraction
features visualization
Finite difference methods
Finite element method
Finite element methods
Fluid flow
Helmholtz-Hodge decomposition
Hydrodynamics
incompressible flow
Mathematical analysis
Mathematics
Meshless methods
Models, Theoretical
multiphase fluids
Poisson equations
Rheology - methods
smoothed particles hydrodynamics
Two dimensional
vector field
Vectors (mathematics)
Visualization
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Summary:Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. This decomposition is usually achieved by using mesh-based methods such as finite differences or finite elements. This work presents a new meshless approach to the Helmholtz-Hodge decomposition for the analysis of 2D discrete vector fields. It embeds into the SPH particle-based framework. The proposed method is efficient and can be applied to extract features from a 2D discrete vector field and to multiphase fluid flow simulation to ensure incompressibility.
ISSN:1077-2626
1941-0506
DOI:10.1109/TVCG.2009.61