Spectral discretization of Darcy’s equations with pressure dependent porosity

We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with boundary conditions on the pressure around a circular well. When the boundary pressure presents high variations, the permeability of the medium depends on the pressure, so that the model is nonl...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-11, Vol.217 (5), p.1838-1856
Main Authors: Azaïez, Mejdi, Ben Belgacem, Faker, Bernardi, Christine, Chorfi, Nejmeddine
Format: Article
Language:English
Subjects:
Axisymmetric domain
Boundaries
Computer Science
Darcy’s equations
Discretization
Estimates
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematics
Nonlinear algebraic and transcendental equations
Numerical Analysis
Numerical analysis. Scientific computation
Optimization
Porosity
Pressure dependent porosity
Sciences and techniques of general use
Spectra
Spectral discretization
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Summary:We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with boundary conditions on the pressure around a circular well. When the boundary pressure presents high variations, the permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a spectral discretization of the resulting system of equations which takes into account the axisymmetry of the domain and of the flow. We prove optimal error estimates and present some numerical experiments which confirm the interest of the discretization. Nous considérons l’écoulement d’un fluide visqueux incompressible dans un milieu poreux rigide lorsque la pression donnée sur la partie de la frontiére correspondant à un puits circulaire présente de fortes variations. La perméabilité du milieu dépend alors de la pression, de sorte que le modèle est non linéaire. Nous proposons une discrétisation spectrale de ce modèle qui tient compte de l’axisymétrie du domaine et de l’écoulement. Nous prouvons des estimations d’erreur optimales et présentons quelques expériences numériques qui confirment l’intérêt de la discrétisation.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.06.014