Decomposição de Helmholtz-Hodge via funções de Green
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Data
2018-10-11
Autores
Cordeiro, José Eduardo
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Universidade Federal do Espírito Santo
Resumo
The Helmholtz-Hodge Decomposition (HHD) describes a vector field as the sum of an incompressible, an irrotational, and a harmonic vector field. Unfortunately, for bounded domains, the HHD is not uniquely defined, traditionally, boundary conditions are imposed to obtain a unique solution, but this imposition may not give a compatible decomposition. This work exposes the natural HHD, which is defined without assuming boundary conditions a priori. Using Green’s functions on an infinite extension of the vector field combined with an influence analysis of the components, it’s possible to generate a unique decomposition without assuming boundary conditions. As a result, it enables a reliable analysis without problems generated by boundary conditions.
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Vector fields , Helmholtz-Hodge decomposition , Boundary conditions , Uniqueness , Harmonic flows , Unicidade , Decomposição de Helmholtz-Hodge , Condições de fronteira , Campos harmônicos