Inhalt

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   Title Page
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   Acknowledgements
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   Zusammenfassung
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   Abstract
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   Contents
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   Nomenclature
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   Notation
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  1 Introduction
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   1.1 State of the Art
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   1.2 Related works
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   1.3 Goal of this Thesis
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   1.4 Structure of this Thesis
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   2 Mathematical models
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   2.1 Concentration measures, velocities and diffusive fluxes
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   2.2 Multicomponent transport equations
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   2.2.1 Maxwell-Stefan equations
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   2.2.2 Nernst-Planck equations
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   2.2.3 Electrical current and Ion transport number
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   2.3 Mixture flow - Incompressible Navier-Stokes equations
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   2.4 Electrodynamics - Maxwell's equations
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   2.5 Conclusion
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   3 Numerical approaches
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   3.1 Lattice Boltzmann method for fluid flows
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   3.1.1 Initial conditions
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   3.1.2 Boundary conditions
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   3.2 Multicomponent lattice Boltzmann method
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   3.2.1 Nonideal liquid mixtures
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   3.2.2 Boundary conditions
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   3.3 Membrane black-box model
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   3.3.1 Assumptions and modeling equations
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   3.4 Lattice Boltzmann method for the electric potential
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   3.4.1 Boundary conditions
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   3.5 Parameterization
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   3.6 Conclusion
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   4 Coupling of Multi-Physics Equations
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   4.1 General set-up for a model of an ED process and its modules
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   4.2 Coupling of multicomponent LBM and membrane model
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   4.2.1 Membrane-electrolyte interface
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   4.3 Coupling of multicomponent LBM and LBM for electric potential
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   4.4 Conclusion
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  5 Simulation framework
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   5.1 Apes overview
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   5.2 Octree data structure
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   5.3 Seeder - Mesh generator
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   5.3.1 Mesh generation with spacer geometry
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   5.4 Musubi - lattice Boltzmann solver
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   5.4.1 Domain decomposition
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   5.4.2 Topology unaware solver data structure
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   5.4.3 Stream-collide algorithm
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   5.4.4 Main program
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   5.4.5 Performance
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   5.5 APESmate - Integrated coupling tool
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   5.5.1 Variable system
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   5.5.2 Space-time function
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   5.5.3 Coupling algorithm
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   5.6 Conclusion
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  6 Numerical validation and verification
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   6.1 Poiseuille flow
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   6.2 Stefan tube
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   6.3 Concentric cylinders
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   6.4 Taylor dispersion
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   6.5 Electrical double layer
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   6.6 Conclusion
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  7 Results
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   7.1 Flow simulations with spacers
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   7.1.1 Spacer geometry
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   7.1.2 Pure hydrodynamic flow
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   7.1.3 Multicomponent flows
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   7.2 Repeating unit in ED stack
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  8 Summary and Future work
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   8.1 Summary
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   8.2 Future work
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  A Appendix
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  A.1 Asymptotic analysis
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   A.1.1 Lattice Boltzmann Method for Fluid Flow
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   A.1.2 Multicomponent Lattice Boltzmann Method for Nonideal Liquid Mixtures
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   A.1.3 Lattice Boltzmann Method for Electric Potential
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   A.1.4 Time Discretization
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  A.2 Multiple Relaxation Time
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   A.2.1 D3Q19 model
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   A.3 Configurations
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   Bibliography
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   List of Figures
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   List of Tables
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   List of Algorithms