title: Meshless helmholtz-hodge decomposition.
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.
authors.affiliation: Universidad Federal do Espírito Santo, Brazil.
authors.forename: Fabiano
authors.initials: F
authors.lastname: Petronetto
authors.forename: Afonso
authors.initials: A
authors.lastname: Paiva
authors.forename: Marcos
authors.initials: M
authors.lastname: Lage
authors.forename: Geovan
authors.initials: G
authors.lastname: Tavares
authors.forename: Hélio
authors.initials: H
authors.lastname: Lopes
authors.forename: Thomas
authors.initials: T
authors.lastname: Lewiner
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D008962:Models, Theoretical; D012212:Rheology / Q000379:methods*