Two-scale Convergence of a Model for Flow in a Partially Fissured Medium
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The distributed-microstructure model for the flow of single phase fluid in a partially fissured composite medium due to Douglas-Peszynska-Showalter  is extended to a quasi-linear version. This model contains the geometry of the local cells distributed throughout the medium, the flux exchange across their intricate interface with the imbedded fissure system, and the secondary flux resulting from diffusion paths within the matrix. Both the exact but highly singular micro-model and the macro-model are shown to be well-posed, and it is proved that the solution of the micro-model is two-scale convergent to that of the macro-model as the spatial parameter goes to zero. In the linear case, the effective coefficients are obtained by a partial decoupling of the homogenized system.