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Issue No. 02 - March/April (2010 vol. 16)
ISSN: 1077-2626
pp: 338-349
Thomas Lewiner , PUC-Rio, Rio de Janeiro
Afonso Paiva , Universidade Federal de Uberlândia, Minas Gerais
Fabiano Petronetto , Universidad Federal do Espírito Santo, Brazil
Geovan Tavares , PUC-Rio, Rio de Janeiro
Hélio Lopes , PUC-Rio, Rio de Janeiro
Marcos Lage , PUC-Rio, Rio de Janeiro
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.
INDEX TERMS
Helmholtz-Hodge decomposition, smoothed particles hydrodynamics, vector field, features visualization, multiphase fluids, incompressible flow.
CITATION
Thomas Lewiner, Afonso Paiva, Fabiano Petronetto, Geovan Tavares, Hélio Lopes, Marcos Lage, "Meshless Helmholtz-Hodge Decomposition", IEEE Transactions on Visualization & Computer Graphics, vol. 16, no. , pp. 338-349, March/April 2010, doi:10.1109/TVCG.2009.61
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