1 Introduction. - 1. 1 Basic Idea. - 1. 2 First Examples. - 1. 3 Diffusion in Periodic Media. - 1. 4 Formal Derivation of Darcy's Law. - 1. 5 Formal Derivation of a Distributed Microstructure Model. - 1. 6 Remarks on Networks of Resistors Capillary Tubes and Cracks. - 2 Percolation Models for Porous Media. - 2. 1 Fundamentals of Percolation Theory. - 2. 2 Exponent Inequalities for Random Flow and Resistor Networks. - 2. 3 Critical Path Analysis in Highly Disordered Porous and Conducting Media. - 3 One-Phase Newtonian Flow. - 3. 1 Derivation of Darcy's Law. - 3. 2 Inertia Effects. - 3. 3 Derivation of Brinkman's Law. - 3. 4 Double Permeability. - 3. 5 On the Transmission Conditions at the Contact Interface between a Porous Medium and a Free Fluid. - 4 Non-Newtonian Flow. - 4. 1 Introduction. - 4. 2 Equations Governing Creeping Flow of a Quasi-Newtonian Fluid. - 4. 3 Description of a Periodic s-Geometry Construction of the Restriction Operator and Review of the Results of Two-Scale Convergence in Lq-Spaces. - 4. 4 Statement of the Principal Results. - 4. 5 Inertia Effects for Non-Newtonian Flows through Porous Media. - 4. 6 Proof of the Uniqueness Theorems. - 4. 7 Uniform A Priori Estimates. - 4. 8 Proof of Theorem A. - 4. 9 Proof of Theorem B. - 4. 10 Conclusion. - 5 Two-Phase Flow. - 5. 1 Derivation of the Generalized Nonlinear Darcy Law. - 5. 2 Upscaling Two-Phase Flow Characteristics in a Heterogeneous Reservoir with Capillary Forces (Finite Peclet Number). - 5. 3 Upscaling Two-Phase Flow Characteristics in a Heterogeneous Core Neglecting Capillary Effects (Infinite Peclet Number). - 5. 4 The Double-Porosity Model of Immiscible Two-Phase Flow. - 6 Miscible Displacement. - 6. 1 Introduction. - 6. 2 Upscaling from the Micro-to the Mesoscale. - 6. 3 Upscaling from the Meso-to the Macroscale. - 6. 4 Discussion. - 7 Thermal Flow. -7. 1 Introduction. - 7. 2 Basic Equations. - 7. 3 Natural Convection in a Bounded Domain. - 7. 4 Natural Convection in a Horizontal Porous Layer. - 7. 5 Mixed Convection in a Horizontal Porous Layer. - 7. 6 Thermal Boundary Layer Approximation. - 7. 7 Conclusion. - 8 Poroelastic Media. - 8. 1 Acoustics of an Empty Porous Medium. - 8. 2 A Priori Estimates for a Saturated Porous Medium. - 8. 3 Local Description of a Saturated Porous Medium. - 8. 4 Acoustics of a Fluid in a Rigid Porous Medium. - 8. 5 Diphasic Macroscopic Behavior. - 8. 6 Monophasic Elastic Macroscopic Behavior. - 8. 7 Monophasic Viscoelastic Macroscopic Behavior. - 8. 8 Acoustics of Double-Porosity Media. - 8. 9 Conclusion. - 9 Microstructure Models of Porous Media. - 9. 1 Introduction. - 9. 2 Parallel Flow Models. - 9. 3 Distributed Microstructure Models. - 9. 4 A Variational Formulation. - 9. 5 Remarks. - 10 Computational Aspects of Dual-Porosity Models. - 10. 1 Single-Phase Flow. - 10. 2 Two-Phase Flow. - 10. 3 Some Computational Results. - A Mathematical Approaches and Methods. - A. 1. 1 F-Convergence. - A. 1. 2 G-Convergence. - A. 1. 3 H-Convergence. - A. 2 The Energy Method. - A. 2. 1 Setting of a Model Problem. - A. 2. 2 Proof of the Results. - A. 3 Two-Scale Convergence. - A. 3. 1 A Brief Presentation. - A. 3. 2 Statement of the Principal Results. - A. 3. 3 Application to a Model Problem. - A. 4 Iterated Homogenization. - B Mathematical Symbols and Definitions. - B. 1 List of Symbols. - B. 2 Function Spaces. - B. 2. 1 Macroscopic Function Spaces. - B. 2. 2 Micro-and Mesoscopic Function Spaces. - B. 2. 3 Two-Scale Function Spaces. - B. 2. 4 Time-Dependent Function Spaces. - C References. Language: English