Some Numerical Methods for Flow and Transport in Fractured Media

Wednesday, January 19, 2000 - 9:30am - 10:00am
Keller 3-180
Jean Roberts (Institut National de Recherche en Informatique Automatique (INRIA))
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.