Multicomponent Flow Modeling

"This book (written with originality by a recognized expert actively working in the title area) can be considered as an interdisciplinary presentation of multicomponent flow models, their mathematical properties, and selected numerical simulations...The book is well organized, clearly written, and can serve as a very useful reference book for specialists (circa 300 contemporary references) and as a good introduction to the subject for senior and graduate-level students in applied mathematics." -Zentralblatt Math

• 1. Introduction.- 2. Fundamental Equations.- 2.1. Introduction.- 2.2. Conservation equations.- 2.3. Thermodynamics.- 2.4. Chemistry.- 2.5. Transport fluxes.- 2.6. Entropy.- 2.7. Boundary conditions.- 2.8. Notes.- 2.9. References.- 3. Approximate and Simplified Models.- 3.1. Introduction.- 3.2. One-reaction chemistry.- 3.3. Small Mach number flows.- 3.4. Coupling.- 3.5. Notes.- 3.6. References.- 4. Derivation from the Kinetic Theory.- 4.1. Introduction.- 4.2. Kinetic framework.- 4.3. Kinetic entropy.- 4.4. Enskog expansion.- 4.5. Zero-order approximation.- 4.6. First-order approximation.- 4.7. Transport linear systems.- 4.8. Notes.- 4.9. References.- 5. Transport Coefficients.- 5.1. Introduction.- 5.2. Transport algorithms.- 5.3. Molecular parameters.- 5.4. Shear viscosity.- 5.5. Volume viscosity.- 5.6. Diffusion matrix.- 5.7. Thermal conductivity.- 5.8. Thermal diffusion ratios.- 5.9. Partial thermal conductivity.- 5.10. Thermal diffusion coefficients.- 5.11. Notes.- 5.12. References.- 6. Mathematics of Thermochemistry.- 6.1. Introduction.- 6.2. Thermodynamics with volume densities.- 6.3. Thermodynamics with mass densities.- 6.4. Chemistry sources.- 6.5. Positive equilibrium points.- 6.6. Boundary equilibrium points.- 6.7. Inequalities near equilibrium.- 6.8. A global stability inequality.- 6.9. Notes.- 6.10. References.- 7. Mathematics of Transport Coefficients.- 7.1. Introduction.- 7.2. Assumptions on transport coefficients.- 7.3. Properties of diffusion matrices.- 7.4. Properties of other coefficients.- 7.5. Diagonal diffusion.- 7.6. Diffusion inequalities.- 7.7. Stefan-Maxwell equations.- 7.8. Notes.- 7.9. References.- 8. Symmetrization.- 8.1. Introduction.- 8.2. Vector notation.- 8.3. Quasilinear form.- 8.4. Symmetrization and entropic variables.- 8.5. Normal forms.- 8.6. Symmetrization for multicomponent flows.- 8.7. Normal forms for multicomponent flows.- 8.8. Notes.- 8.9. References.- 9. Asymptotic Stability.- 9.1. Introduction.- 9.2. Governing equations.- 9.3. Local dissipative structure.- 9.4. Global existence theorem.- 9.5. Decay estimates.- 9.6. Local dissipativity for multicomponent flows.- 9.7. Global existence for multicomponent flows.- 9.8. Notes.- 9.9. References.- 10. Chemical Equilibrium Flows.- 10.1. Introduction.- 10.2. Governing equations.- 10.3. Entropy and symmetrization.- 10.4. Normal forms.- 10.5. Global existence.- 10.6. Notes.- 10.7. References.- 11. Anchored Waves.- 11.1. Introduction.- 11.2. Governing equations.- 11.3. First properties.- 11.4. Existence on a bounded domain.- 11.5. Existence of solutions.- 11.6. Notes.- 11.7. References.- 12. Numerical Simulations.- 12.1. Introduction.- 12.2. Laminar flame model.- 12.3. Computational considerations.- 12.4. Hydrogen-Air Bunsen flame.- 12.5. References.