Multicomponent flow modeling.

*(English)*Zbl 0956.76003
Boston: Birkhäuser. 321 p. (1999).

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 consists of 12 chapters. In chapters 2 to 5, starting from the kinetic theory of gases, the author gives a detailed description of multicomponent flow models, including basic governing equations, thermodynamics, chemical reactions, and practically important expressions for transport coefficients. Chapters 6-11 are aimed primarily at mathematically inclined reader, and treat in the first place purely mathematical properties of the above equations, such as symmetrization, well-posedness and asymptotic stability. Finally, the brief illustrative chapter 12 presents numerical simulations of Bunsen laminar flame model with a typical hydrogen-air combustion mechanism.

The details of the presentation are apparent from the extended table of contents: 1. Introduction; 2. Fundamental equations (conservation equations, thermodynamics, chemistry, transport fluxes, entropy, boundary conditions); 3. Approximate and simplified models (one-reaction chemistry, small Mach number flows, coupling); 4. Derivation from the kinetic theory (kinetic entropy, Enskog expansion, zeroth- and first-order approximations, transport linear systems); 5. Transport coefficients (transport algorithms, molecular parameters, shear and volume viscosity, diffusion matrix, thermal conductivity); 6. Mathematics of thermochemistry (thermodynamics with volume and mass densities, chemistry sources, positive and boundary equilibrium points, inequalities near equilibrium, global stability inequality); 7. Mathematics of transport coefficients (properties of diffusion matrices, diagonal diffusion, Stefan-Maxwell equations); 8. Symmetrization (quasilinear and normal forms); 9. Asymptotic stability (local dissipativity, global existence theorems, decay estimates); 10. Chemical equilibrium flows (entropy and symmetrization, normal forms, global existence); 11. Anchored waves (existence of solution and existence on a bounded domain); 12. 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.

The details of the presentation are apparent from the extended table of contents: 1. Introduction; 2. Fundamental equations (conservation equations, thermodynamics, chemistry, transport fluxes, entropy, boundary conditions); 3. Approximate and simplified models (one-reaction chemistry, small Mach number flows, coupling); 4. Derivation from the kinetic theory (kinetic entropy, Enskog expansion, zeroth- and first-order approximations, transport linear systems); 5. Transport coefficients (transport algorithms, molecular parameters, shear and volume viscosity, diffusion matrix, thermal conductivity); 6. Mathematics of thermochemistry (thermodynamics with volume and mass densities, chemistry sources, positive and boundary equilibrium points, inequalities near equilibrium, global stability inequality); 7. Mathematics of transport coefficients (properties of diffusion matrices, diagonal diffusion, Stefan-Maxwell equations); 8. Symmetrization (quasilinear and normal forms); 9. Asymptotic stability (local dissipativity, global existence theorems, decay estimates); 10. Chemical equilibrium flows (entropy and symmetrization, normal forms, global existence); 11. Anchored waves (existence of solution and existence on a bounded domain); 12. 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.

Reviewer: Oleg Titow (Berlin)

##### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |

76V05 | Reaction effects in flows |

80A25 | Combustion |

76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |

76T30 | Three or more component flows |

92E20 | Classical flows, reactions, etc. in chemistry |

80A32 | Chemically reacting flows |