Homogenization of Coupled Phenomena in Heterogenous Media

Main notations 17

Introduction 21

PART ONE. UPSCALING METHODS 27

Chapter 1. An Introduction to Upscaling Methods 29

Chapter 2. Heterogenous Medium: Is an Equivalent Macroscopic Description Possible? 55

Chapter 3. Homogenization by Multiple Scale Asymptotic Expansions 75

PART TWO. HEAT AND MASS TRANSFER 107

Chapter 4. Heat Transfer in Composite Materials 109

Chapter 5. Diffusion/Advection in Porous Media 143

Chapter 6. Numerical and Analytical Estimates for the Effective Diffusion Coefficient 161

PART THREE. NEWTONIAN FLUID FLOW THROUGH RIGID POROUS MEDIA 195

Chapter 7. Incompressible Newtonian Fluid Flow Through a Rigid Porous Medium 197

Chapter 8. Compressible Newtonian Fluid Flow Though a Rigid Porous Medium 229

Chapter 9. Numerical Estimation of the Permeability of Some Periodic Porous Media 257

Chapter 10. Self-consistent Estimates and Bounds for Permeability 275

PART FOUR. SATURATED DEFORMABLE POROUS MEDIA 337

Chapter 11. Quasi-statics of Saturated Deformable Porous Media 339

Chapter 12. Dynamics of Saturated Deformable Porous Media 367

Chapter 13. Estimates and Bounds for Effective Poroelastic Coefficients 389

Chapter 14. Wave Propagation in Isotropic Saturated Poroelastic Media 407

Bibliography . 453

Index 473