Prologue

Kapitel in diesem Buch

1. Frontmatter I
2. Dedication V
3. Contents VII
4. Prologue 1
5. Chapter 1 Why this monograph? 3
6. Chapter 2 A brief pertinent CFD chronology 6
7. Chapter 3 Fluid mechanics conservation principles, PDE notation 13
8. Part A: Space-time discretization error annihilation, algebraic instability
9. Chapter 4 Legacy CFD difference algebra derived stabilizations, O(h²) truncation error annihilation (TEA) theory, NS error freed PDE mathematics, monotonicity, stability 21
10. Chapter 5 Navier-Stokes error freed CFD mathematics, continuous weak formulation, FE theory, asymptotic convergence, error estimates, validations, monotone continuum shock interpolation 42
11. Chapter 6 Time-averaged (RaNS) Navier-Stokes error freed CFD weak formulation, theory, asymptotic convergence, validations 73
12. Chapter 7 Annihilation of NS/RaNS PDE space-time discretization-induced O(m², m³) phase dispersion and O(Δt³) truncation errors 97
13. Chapter 8 Hypersonics, aerothermodynamics, radiation CFD issues 109
14. Part B: Analytical closure of spatially filtered NS PDE systems
15. Chapter 9 Mathematically rigorous closure of spatially filtered NS PDE systems 125
16. Chapter 10 FaNS theory O(1;δ²) PDE system rendered bounded domain well-posed 139
17. Chapter 11 Validation, FaNS, NS PDE systems same code/mesh predictions,100 < Re < 4,000 159
18. Chapter 12 Validation, ∀ Re pertinent FaNS theory prediction of laminar BL profile O(1) velocity insipient transition, separation, turbulent BL profile reattachment, then relaminarization, Re ≈ 12,000 175
19. Chapter 13 Epilogue, error freed CFD mathematics continuing impact 201
20. Nomenclature
21. Appendix A: The finite element toolbox 207
22. Appendix B: Theory, weak formulation optimal continuous Galerkin FE p = 1,2,3 basis CFD algorithms 221
23. Appendix C: Error freed CFD mathematics altered continuous Galerkin FE basis algorithm and Newton jacobian matrix statements 233
24. Subject index 345