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Talk Abstract:
Some Numerical Techniques For Flow and Transport in Fractured
Porous Media
Jean
Roberts
INRIA-Rocquencourt
B.P. 105
F-78513 Le Chesnay Cedex
FRANCE
email: Jean.Roberts@inria.fr
Joint work with Clarisse Alboin and
Jerome Jaffré of
Inria and Christophe Serre of Ipsn (Institut de Protection et
Sureté Nucléaire)
We
are concerned with the migration of a contaminant, dissolved
in water, in a fractured porous medium. We consider two scales
of fractures: small interconnected fractures, too small and
too numerous to be treated individually and larger fractures
that might be included specifically in the model.
The
smaller fractures are taken into account by a continuous model,
a double porosity model. This model, the issue of homogenization,
resembles the model in a non fractured medium; only a coupling
term, representing the exchange between the fractures and the
matrix blocs, has been added. This term, an operator from H1(0,T;H1 
to L2(0,T;H1 ),
where
is the domain and (0,T) the time interval, can add considerably
to the cost of using this model. Several ways of calculating
this operator are considered; in particular an approximation
to the singular convolution kernel of the analytic solution
leads to an efficient method for the cases considered.
Larger fractures or faults are taken into account with a discrete
model. This model, in which these fractures are treated as interfaces,
is obtained using asymptotic analysis. A nonlocal interface
condition on the fractures yields a nonstandard domain decomposition
problem.
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1999-2000
Reactive Flow and Transport Phenomena
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