3-dimensional physically consistent diffusion in anisotropic media with memory

Michele Caputo

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1998)

  • Volume: 9, Issue: 2, page 131-143
  • ISSN: 1120-6330

Abstract

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Some data on the flow of fluids exhibit properties which may not be interpreted with the classic theory of propagation of pressure and of fluids [21] based on the classic D’Arcy’s law which states that the flux is proportional to the pressure gradient. In order to obtain a better representation of the flow and of the pressure of fluids the law of D’Arcy is here modified introducing a memory formalisms operating on the flow as well as on the pressure gradient which implies a filtering of the pressure gradient without singularities; the properties of the filtering are also described. We shall also modify the second constitutive equation of diffusion, which relates the density variations of the fluid to its pressure variations, by introducing the rheology of the fluid also represented by derivatives of fractional order operating on the pressure as well as on the density. Moreover the medium will be considered anisotropic. We shall obtain the diffusion equation with these conditions in an anisotropic medium and find the Green function for a point source.

How to cite

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Caputo, Michele. "3-dimensional physically consistent diffusion in anisotropic media with memory." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.2 (1998): 131-143. <http://eudml.org/doc/252300>.

@article{Caputo1998,
abstract = {Some data on the flow of fluids exhibit properties which may not be interpreted with the classic theory of propagation of pressure and of fluids [21] based on the classic D’Arcy’s law which states that the flux is proportional to the pressure gradient. In order to obtain a better representation of the flow and of the pressure of fluids the law of D’Arcy is here modified introducing a memory formalisms operating on the flow as well as on the pressure gradient which implies a filtering of the pressure gradient without singularities; the properties of the filtering are also described. We shall also modify the second constitutive equation of diffusion, which relates the density variations of the fluid to its pressure variations, by introducing the rheology of the fluid also represented by derivatives of fractional order operating on the pressure as well as on the density. Moreover the medium will be considered anisotropic. We shall obtain the diffusion equation with these conditions in an anisotropic medium and find the Green function for a point source.},
author = {Caputo, Michele},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Diffusion; Filtering; Anisotropy; Memory; D’Arcy; modified Darcy law; anisotropic media; fluid rheology; filtering of pressure gradient; Green function for point source; memory formalism; constitutive equation of diffusion; derivatives of fractional order},
language = {eng},
month = {6},
number = {2},
pages = {131-143},
publisher = {Accademia Nazionale dei Lincei},
title = {3-dimensional physically consistent diffusion in anisotropic media with memory},
url = {http://eudml.org/doc/252300},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Caputo, Michele
TI - 3-dimensional physically consistent diffusion in anisotropic media with memory
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/6//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 2
SP - 131
EP - 143
AB - Some data on the flow of fluids exhibit properties which may not be interpreted with the classic theory of propagation of pressure and of fluids [21] based on the classic D’Arcy’s law which states that the flux is proportional to the pressure gradient. In order to obtain a better representation of the flow and of the pressure of fluids the law of D’Arcy is here modified introducing a memory formalisms operating on the flow as well as on the pressure gradient which implies a filtering of the pressure gradient without singularities; the properties of the filtering are also described. We shall also modify the second constitutive equation of diffusion, which relates the density variations of the fluid to its pressure variations, by introducing the rheology of the fluid also represented by derivatives of fractional order operating on the pressure as well as on the density. Moreover the medium will be considered anisotropic. We shall obtain the diffusion equation with these conditions in an anisotropic medium and find the Green function for a point source.
LA - eng
KW - Diffusion; Filtering; Anisotropy; Memory; D’Arcy; modified Darcy law; anisotropic media; fluid rheology; filtering of pressure gradient; Green function for point source; memory formalism; constitutive equation of diffusion; derivatives of fractional order
UR - http://eudml.org/doc/252300
ER -

References

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