Preface -- Upscaled models for CO2 injection and migration in geological systems -- 1 Introduction -- 2 Background -- 3 Model description -- 3.1 Key assumptions and dimensionless groupings -- 3.2 Vertical fluid and pressure distribution -- 3.3 Model derivation -- 3.4 Upscaling and subscale processes -- 4 Model application -- 5 Summary -- Multipoint flux approximation L-method in 3D: numerical convergence and application to two-phase flow through porous media -- 1 Introduction -- 2 The MPFA L-method in 3D -- 2.1 Details of the scheme -- 2.2 Criterion for choosing the proper L-stencil -- 2.3 Boundary handling -- 3 Numerical convergence -- 3.1 Benchmark test 1 -- 3.2 Benchmark test 3 -- 4 Grid adaptivity -- 4.1 Boundary handling -- 5 Two-phase flow applications -- 5.1 Two-phase model description -- 5.2 Buckley-Leverett-type problem -- 5.3 McWhorter-type problem -- 5.4 DNAPL infiltration problem -- 5.5 Refinement and coarsening indicator -- 6 Summary and conclusions -- Compositional two-phase flow in saturated-unsaturated porous media: benchmarks for phase appearance/disappearance -- 1 Introduction -- 2 Definition and basic assumptions -- 3 Equations -- 3.1 Mass conservation of each component -- 4 Choice of the primary variables -- 5 Presentation of the two test cases -- 5.1 First test case: gas phase appearing/disappearing by gas injection in a water-saturated rock core sample -- 5.2 Second test case: evolution from an initial out of equilibriumstate to a stabilized stationary one, in a sealed porous core sample -- 6 Conclusions and perspectives -- Coupling free and porous-media flows: models and numerical approximation -- 1 Introduction -- 2 Setting of the problem -- 2.1 The surface-groundwater flow problem -- 2.2 Interface conditions to couple surface and groundwater flows -- 3 Weak formulation and analysis.

3.1 Mixed formulation of Darcy's equation -- 3.2 Time-dependent Stokes/Darcy model -- 4 Multidomain formulation of the coupled problem -- 4.1 The Stokes/Darcy problem -- 4.2 The Navier-Stokes/Darcy problem -- 4.3 Well-posedness of the interface problems -- 5 Finite element approximation of free and porous-media flows -- 5.1 Galerkin finite-element approximation of the Stokes/Darcy problem -- 6 Algebraic formulation of the linear interface problem and solution techniques -- 6.1 Numerical results -- 6.2 Other preconditioning methods -- 7 Iterative methods for the Navier-Stokes/Darcy problem -- 8 Subdomain iterative methods for the time-dependent (Navier-)Stokes/Darcy problem -- Mathematical and numerical modeling of flow, transport, and reactions in porous structures of electrochemical devices -- 1 Introduction -- 1.1 Model scales -- 1.2 The direct methanol fuel cell - an example of an electrochemical device with a porous electrode -- 2 Electrolytes and interfaces -- 2.1 Dilute electrolytes -- 2.2 Bulk electroneutrality -- 2.3 Double layer -- 2.4 Interface between electrode and electrolyte -- 2.5 Faradaic reactions -- 3 Porous electrodes -- 3.1 Ideally polarizable porous matrix -- 3.2 Species transport -- 3.3 Darcy flow -- 3.4 Further effects -- 3.5 Coupling between porous electrodes and free flow -- 4 Numerical approximation by Voronoi finite volumes -- 4.1 Description of the method -- 4.2 Flux expressions for scalar convection diffusion -- 4.3 Coupling to flow problems -- 4.4 Software -- 5 Conclusions -- Multiscale modeling of flow and geomechanics -- 1 Introduction -- 2 Background -- 2.1 Multidomain methodology -- 2.2 Discretization methods -- 2.3 Coupled flow and geomechanics -- 3 Multiscale multiphysics discretizations for flow and geomechanics.

4 Multiscale domain decomposition solvers and preconditioners -- 5 A posteriori error estimation and time-stepping -- 6 Uncertainty quantification, verification, and validation -- 7 Applications -- 7.1 Compositional modeling of multiphase flow -- 7.2 Fixed stress iterative coupling scheme -- 7.3 Plasticity modeling -- 8 Summary and conclusions -- List of contributors -- Index.