From Stokes Flow to Darcy’s Law Cna Working Group on Homogenization – Spring
نویسنده
چکیده
Contents 1. Introduction 2 1.1. Porous media 2 1.2. Defining the microstructure 2 1.3. Darcy's law 3 2. Function spaces 4 2.1. Definitions 4 2.2. Some properties 5 3. Pressure as a Lagrange multiplier 5 3.1. A splitting of H 1 0 (Γ) 5 3.2. Finding the pressure 7 4. Solving the Stokes problem 7 5. Technical preliminaries for Darcy's law 9 5.1. The Poincaré inequality in Ω ε 9 5.2. Extension and restriction operators 10 6. Deriving Darcy's law 14 6.1. The cell problem and the permeability tensor 14 6.2. Darcy's law 15 References 21
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