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darcy’s equations

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Automatic simplification of Darcy’s equations with pressuredependent permeability
Etienne Ahusborde, Mejdi Azaïez, Faker Ben Belgacem, Christine Bernardi
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 47 / Issue 6 / November 2013

Published online by Cambridge University Press:

07 October 2013, pp. 1797-1820

Print publication:

November 2013
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We consider the flow of a viscous incompressible fluid in a rigid homogeneous porousmedium provided with mixed boundary conditions. Since the boundary pressure can presenthigh variations, the permeability of the medium also depends on the pressure, so that themodel is nonlinear. A posteriori estimates allow us to omit thisdependence where the pressure does not vary too much. We perform the numerical analysis ofa spectral element discretization of the simplified model. Finally we propose a strategywhich leads to an automatic identification of the part of the domain where the simplifiedmodel can be used without increasing significantly the error.