Homogenized double porosity models for poro-elastic media with interfacial flow barrier

Abdelhamid Ainouz

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 4, page 357-365
  • ISSN: 0862-7959

Abstract

top
In the paper a Barenblatt-Biot consolidation model for flows in periodic porous elastic media is derived by means of the two-scale convergence technique. Starting with the fluid flow of a slightly compressible viscous fluid through a two-component poro-elastic medium separated by a periodic interfacial barrier, described by the Biot model of consolidation with the Deresiewicz-Skalak interface boundary condition and assuming that the period is too small compared with the size of the medium, the limiting behavior of the coupled deformation-pressure is studied.

How to cite

top

Ainouz, Abdelhamid. "Homogenized double porosity models for poro-elastic media with interfacial flow barrier." Mathematica Bohemica 136.4 (2011): 357-365. <http://eudml.org/doc/196774>.

@article{Ainouz2011,
abstract = {In the paper a Barenblatt-Biot consolidation model for flows in periodic porous elastic media is derived by means of the two-scale convergence technique. Starting with the fluid flow of a slightly compressible viscous fluid through a two-component poro-elastic medium separated by a periodic interfacial barrier, described by the Biot model of consolidation with the Deresiewicz-Skalak interface boundary condition and assuming that the period is too small compared with the size of the medium, the limiting behavior of the coupled deformation-pressure is studied.},
author = {Ainouz, Abdelhamid},
journal = {Mathematica Bohemica},
keywords = {homogenization; porelasticity; two-scale convergence; homogenization; poro-elasticity; two-scale convergence},
language = {eng},
number = {4},
pages = {357-365},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homogenized double porosity models for poro-elastic media with interfacial flow barrier},
url = {http://eudml.org/doc/196774},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Ainouz, Abdelhamid
TI - Homogenized double porosity models for poro-elastic media with interfacial flow barrier
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 4
SP - 357
EP - 365
AB - In the paper a Barenblatt-Biot consolidation model for flows in periodic porous elastic media is derived by means of the two-scale convergence technique. Starting with the fluid flow of a slightly compressible viscous fluid through a two-component poro-elastic medium separated by a periodic interfacial barrier, described by the Biot model of consolidation with the Deresiewicz-Skalak interface boundary condition and assuming that the period is too small compared with the size of the medium, the limiting behavior of the coupled deformation-pressure is studied.
LA - eng
KW - homogenization; porelasticity; two-scale convergence; homogenization; poro-elasticity; two-scale convergence
UR - http://eudml.org/doc/196774
ER -

References

top
  1. Ainouz, A., Derivation of a convection process in a steady diffusion-transfer problem by homogenization, Int. J. Appl. Math. 21 (2008), 83-97. (2008) Zbl1144.35329MR2408055
  2. Allaire, G., 10.1137/0523084, SIAM J. Math. Anal. 23 (1992), 1482-15192. (1992) Zbl0770.35005MR1185639DOI10.1137/0523084
  3. Allaire, G., Damlamian, A., Hornung, U., Two scale convergence on periodic surfaces and applications, Proceedings of the International Conference on Mathematical Modelling of Flow through Porous Media (May 1995) A. Bourgeat et al. (1996), 15-25 World Scientific Singapore. (1996) 
  4. Barenblatt, G., Zheltov, Y., Kochina, I., On basic concepts of the theory of homogeneous fluids seepage in fractured rocks, Russian Prikl. Mat. Mekh. 24 (1960), 852-864. (1960) 
  5. Biot, M., 10.1063/1.1712886, J. Appl. Physics 12 (1941), 155-164. (1941) DOI10.1063/1.1712886
  6. Biot, M., Willis, D., The elasticity coefficients of the theory of consolidation, J. Appl. Mech. 24 (1957), 594-601. (1957) MR0092472
  7. Deresiewicz, H., Skalak, R., On uniqueness in dynamic poroelasicity, Bull. Seismol. Soc. Amer. 53 (1963), 783-788. (1963) 
  8. Ene, H., Poliševski, D., 10.1007/PL00013849, Z. Angew. Math. Phys. 53 (2002), 1052-1059. (2002) Zbl1017.35016MR1963553DOI10.1007/PL00013849
  9. Showalter, R., Momken, B., 10.1002/mma.276, Math. Methods Appl. Sci. 25 (2002), 115-139. (2002) Zbl1097.35067MR1879654DOI10.1002/mma.276
  10. Wilson, R., Aifantis, E., 10.1016/0020-7225(82)90036-2, Int. J. Eng. Sci. 20 (1982), 1009-1035. (1982) Zbl0493.76094DOI10.1016/0020-7225(82)90036-2

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.