Multicomponent transport algorithms

✍ Scribed by Alexandre Ern; Vincent Giovangigli

• Publisher: Springer-Verlag
• Year: 1994
• Tongue: English
• Leaves: 441
• Series: Lecture notes in physics., New series m,, Monographs ;, m24
• Category: Library

✦ Synopsis

This book presents a general and self-contained theory of iterative algorithms for evaluating transport coefficients of dilute polyatomic gas mixtures, including the Enskog-Chapman procedure with its extension to reactive mixtures, the variational framework for polynomial expansions, the mathematical properties of the linear systems, the singular case of vanishing concentrations, iterative methods with convergence theorems, and explicit, accurate, approximate expressions for all the transport coefficients.This book contains mostly new developments and is written for the broadest audience of potentially interested readers, including engineers, physicists, chemists, numerical modelers, applied mathematicians, and mathematicians. Therefore, every mathematical step is carefully explained and only introductory linear algebra and kinetic theory concepts are needed.The authors made a special effort in presenting the material rigorously and comprehensively, thereby providing a complete source of reference for evaluating multicomponent transport coefficients. Read more... 1. Introduction. 1.1. Detailed Modeling of Dilute Polyatomic Gas Mixtures -- 2. Transport Linear Systems. 2.1. Transport Coefficients of Dilute Polyatomic Gas Mixtures. 2.2. Derivation of the Transport Linear Systems. 2.3. Mathematical Structure of the Transport Linear Systems. 2.4. The Shear Viscosity. 2.5. The Volume Viscosity. 2.6. The Diffusion Matrix. 2.7. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 2.8. The Thermal Conductivity and the Thermal Diffusion Ratios. 2.9. Comparison with the Systems of Monchick, Yun, and Mason. 2.10. The Mason and Monchick approximations -- 3. Rescaled Transport Linear Systems. 3.1. Transport Linear System for Nonnegative Mass Fractions. 3.2. The Shear Viscosity. 3.3. The Volume Viscosity. 3.4. The Flux Diffusion Matrix. 3.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 3.6. The Thermal Conductivity and the Thermal Diffusion Ratios. 3.7. The Mason and Monchick Approximations -- 4. Mathematical Properties. 4.1. Mathematical Preliminaries. 4.2. The Shear Viscosity. 4.3. The Volume Viscosity. 4.4. The Diffusion Matrix and the Flux Diffusion Matrix. 4.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 4.6. The Thermal Conductivity and the Thermal Diffusion Ratios. 4.7. The Dilution Limit -- 5. Convergent Iterative Methods. 5.1. Iterative Methods for Constrained Singular Systems. 5.2. The Shear Viscosity. 5.3. The Volume Viscosity. 5.4. The Diffusion Matrix and the Flux Diffusion Matrix. 5.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 5.6. The Thermal Conductivity and the Thermal Diffusion Ratios -- 6. Numerical Experiments. 6.1. Computational Considerations. 6.2. The Shear Viscosity. 6.3. The Volume Viscosity. 6.4. The Diffusion Matrix and the Flux Diffusion Matrix. 6.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 6.6. The Thermal Conductivity and the Thermal Diffusion Ratios -- 7. Concluding Remarks

✦ Table of Contents

Lecture Notes in Physics: Monographs 24 ......Page 1
Multicomponent Transport Algorithms ......Page 3
Preface ......Page 5
Contents ......Page 7
1.1. Detailed Modeling of Dilute Polyatomic Gas Mixtures ......Page 15
1.2. Outline of Subsequent Chapters ......Page 18
2. Transport Linear Systems ......Page 23
2.1. Transport Coefficients of Dilute Polyatomic Gas Mixtures ......Page 24
2.2. Derivation of the Transport Linear Systems ......Page 47
2.3. Mathematical Structure of the Transport Linear Systems ......Page 55
2.4. The Shear Viscosity ......Page 77
2.5. The Volume Viscosity ......Page 79
2.6. The Diffusion Matrix ......Page 88
2.7. The Partial Thermal Conductivity and the Thermal Diffusion Vector ......Page 96
2.8. The Thermal Conductivity and the Thermal Diffusion Ratios ......Page 100
2.9. Comparison with the Systems of Monchick, Yun, and Mason ......Page 106
2.10.The Mason and Monchick approximations ......Page 113
3. Rescaled Transport Linear Systems ......Page 119
3.1. Transport Linear System for Nonnegative Mass Fractions ......Page 120
3.2. The Shear Viscosity ......Page 149
3.3. The Volume Viscosity ......Page 150
3.4. The Flux Diffusion Matrix ......Page 156
3.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector ......Page 168
3.6. The Thermal Conductivity and the Thermal Diffusion Ratios ......Page 170
3.7. The Mason and Monchick Approximations ......Page 174
4. Mathematical Properties ......Page 179
4.1. Mathematical Preliminaries ......Page 180
4.2. The Shear Viscosity ......Page 187
4.3. The Volume Viscosity ......Page 192
4.4. The Diffusion Matrix and the Flux Diffusion Matrix ......Page 204
4.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector ......Page 235
4.6. The Thermal Conductivity and the Thermal Diffusion Ratios ......Page 245
4.7. The Dilution Limit ......Page 259
5. Convergent Iterative Methods ......Page 265
5.1. Iterative Methods for Constrained Singular Systems ......Page 266
5.2. The Shear Viscosity ......Page 286
5.3. The Volume Viscosity ......Page 291
5.4. The Diffusion Matrix and the Flux Diffusion Matrix ......Page 302
5.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector ......Page 320
5.6. The Thermal Conductivity and the Thermal Diffusion Ratios ......Page 330
6. Numerical Experiments ......Page 343
6.1. Computational Considerations ......Page 344
6.2. The Shear Viscosity ......Page 353
6.3. The Volume Viscosity ......Page 358
6.4. The Diffusion Matrix and the Flux Diffusion Matrix ......Page 366
6.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector ......Page 380
6.6. The Thermal Conductivity and the Thermal Diffusion Ratios ......Page 393
7. Concluding Remarks ......Page 407
Appendix A ......Page 409
Appendix B ......Page 411
Appendix C ......Page 415
Appendix D ......Page 419
Appendix E ......Page 421
Bibliography ......Page 427
Index ......Page 437