Two-scale Convergence of a Model for Flow in a Partially Fissured Medium
Date
1999-01-14
Authors
Clark, G. W.
Showalter, Ralph
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
The distributed-microstructure model for the flow of single phase fluid in a partially fissured composite medium due to Douglas-Peszynska-Showalter [12] 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.
Description
Keywords
Fissured medium, Homogenization, Two-scale convergence, Dual permeability, Modeling, Microstructure
Citation
Clark, G. W., & Showalter, R. E. (1999). Two-scale convergence of a model for flow in a partially fissured medium. <i>Electronic Journal of Differential Equations, 1999</i>(02), pp. 1-20.
Rights
Attribution 4.0 International