Meshless Helmholtz-Hodge decomposition
Fabiano Petronetto, Afonso Paiva, Marcos Lage, Geovan Tavares, Hélio Lopes, Thomas Lewiner
Abstract:
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.Downloads:
PDF paper (20.2 MB)
BibTeX:
@article{sph_hh_tvcg,author = {Fabiano Petronetto and Afonso Paiva and Marcos Lage and Geovan Tavares and Hélio Lopes and Thomas Lewiner},
title = {Meshless Helmholtz-Hodge decomposition},
year = {2010},
month = {march},
journal = {Transactions on Visualization and Computer Graphics},
volume = {16},
number = {2},
pages = {338--342},
publisher = {IEEE},
doi = {10.1109/TVCG.2009.61},
url = {\url{http://thomas.lewiner.org/pdfs/sph_hh_tvcg.pdf}}
}