Groundwater flow in a fissurised porous stratum

Michiel Bertsch; Carlo Nitsch; Michiel Bertsch; Carlo Nitsch

doi:10.3934/nhm.2010.5.765

Networks and Heterogeneous Media

2010, Volume 5, Issue 4: 765-782. doi: 10.3934/nhm.2010.5.765

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Groundwater flow in a fissurised porous stratum

Michiel Bertsch ^{1
,},
Carlo Nitsch ^{2
,}

1.
Istituto per le Applicazioni del Calcolo "M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Roma
2.
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia, Monte S. Angelo, I-80126 Napoli

Received: 01 February 2010
Primary: 35K55; Secondary: 35B30, 35Q35, 35R35, 76S05.

In [2] Barenblatt e.a. introduced a fluid model for groundwater flow in fissurised porous media. The system consists of two diffusion equations for the groundwater levels in, respectively, the porous bulk and the system of cracks. The equations are coupled by a fluid exchange term. Numerical evidence in [2, 8] suggests that the penetration depth of the fluid increases dramatically due to the presence of cracks and that the smallness of certain parameter values play a key role in this phenomenon. In the present paper we give precise estimates for the penetration depth in terms of the smallness of some of the parameters.
- Groundwater flow,
- fissurized porous medium,
- system of partial differential equations,
- free boundary
Citation: Michiel Bertsch, Carlo Nitsch. Groundwater flow in a fissurised porous stratum[J]. Networks and Heterogeneous Media, 2010, 5(4): 765-782. doi: 10.3934/nhm.2010.5.765

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Abstract

In [2] Barenblatt e.a. introduced a fluid model for groundwater flow in fissurised porous media. The system consists of two diffusion equations for the groundwater levels in, respectively, the porous bulk and the system of cracks. The equations are coupled by a fluid exchange term. Numerical evidence in [2, 8] suggests that the penetration depth of the fluid increases dramatically due to the presence of cracks and that the smallness of certain parameter values play a key role in this phenomenon. In the present paper we give precise estimates for the penetration depth in terms of the smallness of some of the parameters.

References

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[8]	Y. Shvets, "Problems of Flooding in Porous and Fissured Porous Rock," Ph.D. thesis, University of California, Berkeley, 2005, http://gradworks.umi.com/31/87/3187151.html.
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